FABLES 


FOR 


ROOF  FRAMING  ETC 


TREATISE 

L^~"~" 


Mathematical  and 
Graphical 


ROOF  FRAMING 


(Illustrated) 


Builders,  Carpenters  and 
Iron  Workers 


D.    INSKIP 

PHILADELPHIA 


Copyright,  1900,  by  6.  D.  Inskip. 


PREFACE 


This  work  is  designed  to  lessen  the  difficulty 
of  angular  computation,  as  in  roof  framing,  etc., 
where  the  hypothenuse  of  a  right  angled  triangle 
is  essential.  The  systems  now  in  vogue  among 
the  laymen  are  of  an  intricate  nature,  and  the 
student  is  apt  to  get  discouraged  with  the  multi- 
plicity of  lines  used  to  obtain  a  nominal  result. 
The  writer  has  experienced  some  of  the  difficul- 
ties and  inconveniences  from  the  scale  systems, 
that  urged  him  to  search  for  a  definite  and  accu- 
rate system,  and  having  been  successful  through 
several  years  of  research  has  been  constrained 
to  publish  the  same  for  the  benefit  of  his  feHow 
craftsmen.  This  system  is  based  on  the  Pytha- 
gorean theorem,  the  sum  of  the  squares  of  the 
two  sides  are  equal  to  the  squares  of  the 
greater  side  or  hypothenuse.  The  tables  are  in 
three  measurements,  viz :  feet,  inches,  eighths ; 
feet,  hundreth  feet;  feet,  inches,  tenths,  com- 
mencing with  £  inch,  y-^  foot,  ^  inch  and 
advancing  to  150  feet,  144  feet,  120  feet 
respectively  in  column  I,  II,  IV.  This  table  is 
called  Tables  of  Reductions  and  Squares.  The 
second  table  is  called  Angular  Ratios,  for  its  deal- 
ing with  degrees,  minutes,  etc.  (commonly 
known  to  be  sines  and  cosines),  but  have  been 
tabulated  altitude  and  base,  and  gives  the  ratios 
for  every  degree  and  minute  in  the  quadrant. 
The  third  table  is  called  Table  of  Pitches,  and 
are  multipliers,  commencing  at  1  inch  per  foot 
base,  and  advancing  by  ^  per  inch  rise  to  1  foot 
6  inches  rise  per  foot. 

G.  D.  INSKIP. 


Table  of  Reductions  and 
Squares 


Column  I  contains  every  dimension  from  | 
inch  to  150  feet,  expressed  in  feet,  inches  and 
eighths  of  inches.  Column  IV  contains  every 
dimension  from  Jg-  inch  to  120  feet,  expressed 
in  feet,  inches  and  tenths  of  inches. 

Column  II  contains  numbers  which  run  in 
sequence  from  1  to  14400,  each  being  the  num- 
ber of  eighth-inches  in  the  dimension  immedi- 
ately at  its  left,  or  the  number  of  tenth-inches 
in  the  dimension  which  stands  opposite  in  col- 
umn IV.  For  instance,  the  first  dimension  in 
Column  I  is  ^  inch.  In  one  inch  there  are  8 
eighths  (Column  II).  But  in  1  inch  there  are 

10  tenths,  hence  1   inch  in   Column  IV  is  not 
opposite  1  inch  in   Column  I,  but  is  two   lines 
lower,  opposite  the  figure  10  in  Column  II.     It 
will  thus  be  seen  that  any  dimensions  in  Column 
I  is  opposite  a  smaller  dimension  in  Column  IV. 
The  relation  between  these  two  opposite  num- 
bers is  immaterial  since   Columns  II  and  IV 
cannot  both  be  used  in  the  same  computation. 

Column  III  contains  the  square  of  every 
whole  number  from  8  to  14,400,  each  number 
in  this  column  being  the  square  of  the  one 
adjoining  in  Column  II.  The  following  problems 
illustrate  some  of  the  uses  of  this  table. 

A  certain  rafter — length,  13'  5f",  is  to  be 
divided  by  8  in  order  to  find  the  length  of  7 
cripple  rafters.  ™&!L  =  (by  Column  II)  !?> 
=  16 If  (eighth-inches).  Pass  along  Column 

11  until  161  is  reached;  adjoining  this  in   Col- 
umn I  is  seen  1'  8J".     Then  the  first  cripple  is 
1'  8J"  in  length.     This  measurement,  however, 
is  f  of  $  of  an  inch  =  /T  of  an  inch  less  than 
is  represented  by  16 If,  which   is  close  enough 
in  practice.     But  as  this  dimension  is  multiplied- 


in  order  to  find  the  length  of  the  longer  cripples, 
the  error  is  also  multiplied.  For  the  second 
cripple  the  error  is  -/-%,  and  so  on  until  8  X  1'  8 \" 
=  13'  5",  which  is  f"  shorter  than  the  original 
dimension. 

This  error  can  be  confined  to  less  than  |"  in 
any  one  piece  by  performing  all  computations 
in  eighths.  For  example,  the  first  cripple 
=  161f ;  the  2d  =  2  X  161f  =  322f ;  the 
3d  =  3  X  161f  =  484| ;  the  4th  =  4  X  161  f 
=  6451 ;  the  5th  =  806| ;  the  6th  ==  968J  ; 
the  7th  =  1129f  and  the  8th  =  1291.  Find 
each  of  these  numbers  in  Column  II,  and  ad- 
joining each,  in  Column  I  is  the  required  crip- 
ple length.  322|  is  nearer  in  value  to  323  than 
to  322,  hence  323  is  taken  and  is  found  equal  to 
3'  4f".  The  other  lengths  are  5'  0£",  6'  8f  ", 
8'  4f",  10'  V,  11'  91",  in  each  of  which  the 
error  is  not  over  -jig-  inch. 

The  fraction,  however,  may  be  carried  to  -^ 
or  less.  For  example,  322|  eighths  =  3'  4£" 
+  f  of  I"  =  3'  4i£" ;  6451  ==  6'  8f  "  +  1 
of  i"  =6'  8J1-",  etc. 

Take  a  similar  problem  in  feet,  inches  and 
tenths: 

A  rafter— length,  15'  3.4",  is  divided  by  9 
in  order  to  find  8  cripple  lengths.  -5>  1A"  =  (by 
Column  IV  and  II)  f-4  =  203f  Then  the 
cripple  lengths  are  407f  =  3'  4.7|  =  3'  4.755", 
611i  —  5/  1.133",  8151  — :  6'  9.511",  1018| 
=  8'  5.888",  1222f  =  10'  2.266",  1426-f  = 
11'  10.644",  16301  =  is/  7.011". 

The  Column  of  Eighths  and  Tenths  is  also 
valuable  in  reducing  complicated  ratios,  such  as 
13'  7f"  to  V  10i"  This  becomes  by  refer- 
ence to  the  table,  1309  to  753.  If  the  ratio  is 
to  be  used  for  determining  bevels,  it  may  be  still 
further  reduced  by  dividing  by  10  or  100.  Then 
1309  to  753  =  13.09  to  7.53  =  (approximately 
13"  to  7i". 

Column  of  Squares 

The  chief  use  made  of  Column  III  in  this 
-work  is  in  the  determination  of  one  side  of  a 


right  angled  triangle  when  the  other  sides  are 

known.     This  is  made  possible  by  the  well  known 

proposition  of  Geometry,  that  the  sum  of  the 

squares  of  the  short  sides   of  a   right   angled 

triangle  equals  the  square  of  the  hypothenuse. 

The  square  of  (a)  plus  the 

square  of  (b)  =  the  square 

of  (c1) ;  hence  the  square  of 

(c)minus  the  square  of  either 

short  side  =  the  square  of 

the  other.     If  (,-)  =   13' 

9j"and(6)  =  11' 3f",  the  length  of  (a)  is  found 

as  follows : 

13'  9i"  (Col.  I)  =  1321, 

whose  square  is  1745041  (Col.  III). 
11'  3f"  (Col.  I)  =  1087, 

whose  square  is  1181569  (Col.  III). 
Their  difference  is  563472.        Passing 

down  Column  III  it  will  be  found  that  there  is 
no  such  number  there ;  the  nearest  to  it  in  value 
is  ."><  ;:>•">(  )0,  which  is  the  square  of  750,  whose 
value  in  feet  and  inches  is  7'  Of".  Then  (a) 
is  less  than  £"  over  7'  Of". 

Xotc  that  no  use  was  made  of  the  numbers 
1321    and   1087.      They   may  be   omitted   in 


Tabular  Difference 

The  difference  between  any  two  successive 
squares  equals  the  sum  of  the  numbers  of  which 
they  are  squares.  This  is  called  the  Tabular 
Difference.  It  is  used  as  follows: 

\\  <•  noted  in  the  problem  above  that  the  value 
of  (#)  is  a  little  over  750  because  the  square  is 
a  little  greater  than  the  square  of  750.  The 
difference  l><t\\cen  these  squares  is  563472  — 
r,i;-jr,()0  =  972.  The  tabular  difference  =  7  <  > 
+  751  =  ir,0i. .  Then  (,/)  =  :  7.">o  :  /.-,;-',  of 
£":  7'9f"  +  £". 

This  operation  is  only  approximately  true, 

since  the  square  of  20|  (for  example)  is  not 
midway  between  the  square  of  'JO  and  '2  1 .  The 
proportion  <  " 


becomes  less  as    the  number   becomes   greater. 
Following  is  an   example    in   feet,   inches  and 
tenths  :   Let  (a)  =  15'  3.8"  and  (b)  =  10'  7.2". 
The  square  of  15'  3.8"  =  3,378,244 
The  square  of  10'  7.2"  ==  1,617,984 

The  sum  of  the  square  is  4,996,228.  The 
number  next  less  than  this  in  Column  III  is 
4995225  and  the  difference  between  them  is 
1003.  The  tabular  difference  =  2235  (see 
Column  II)  +  2236  =  4471.  Then(c)  =  2235 
-j-  ~.  This  is  the  value  of  (e)  in  tenth  inches 
and  equals  approximately  2235.25  =  (Column 
IV)  18'  7,525". 


Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.  Inches 
and  Eighths 

Eixhths 

and 
Teuths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

0 

OJ 

1 

1 

0 

0  1 

0 

oj 

2 

4 

0 

0.2 

0 

3 

9 

0 

0.3 

0 

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16 

0 

0.4 

0 

«;            5 

26 

0 

0.5 

0 

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36             0 

0.6 

0 

01                 ~                      49             0 

0.7 

0 

1                   8 

64            0 

0.8 

0 

U 

9 

81 

0 

0.9 

0 

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10 

100 

0 

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0 

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121 

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if 

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484 

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3i               28 

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:::               29 

841 

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30 

900 

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4                 32 

1024 

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3.9 

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Q 

5* 

46 

2116 

0 

4.6 

0 

47 

2209 

0 

1.7 

0 

6 

48 

2304 

0 

4.8 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 

Feet 

Inches 

0 

6J 

49                    2401              0 

4.9 

0 

6} 

50                    2500              0 

5.0 

0 

6| 

51                    2601             0 

5.1 

0 

6* 

52                   2704             0 

5.2 

0 

61 

53                  2809 

0 

5.3 

0 

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54                   2916 

0 

5.4 

0 

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55                   3025     }         0 

5.5 

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7 

56                   3136 

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0 

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57                  3249 

0 

5.7 

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71 

58                   3364 

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59                   3481 

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5.9 

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60                   3600 

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61                   3721 

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62                   3844 

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6.2 

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63                   3969 

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64     i               4096 

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70                   4900 

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9.6 

Tables  of  Reductions  and  Squares 

1  II  III  IV 


Feet, 
and  ] 

Inches 

Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet, 
and' 

Inches 
rentha 

Feet 

Inches 

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Inches 

1 

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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet.  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

1 

6* 

145 

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1 

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146 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.  Inches 
and  Eighths 

Eighth* 

and 
Tenths 

of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

2 

OJ 

193       37249 

1 

7.3 

2 

H 

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7-4 

2 

0| 

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2 

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0! 

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I  II  III  IV 


Feet,  Inches 
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Eighths 
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iii 

1534 

2353156 

12 

9.4 

15 

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1535 

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12 

9.5 

16 

0 

1536 

2359296 

12 

9.6 

Tables  of  Reductions  and  Squares 

I  II  III  IT 


Eighths  ! 
Feet,  Inches     and 
and  EiRhtns    Tenths 

SQUARES 

Feet,  Inches 
and  Tenths 

of  Inches 

Feet 

Inches 

Feet 

Inches 

16 

o* 

1537 

2362369 

12 

9.7 

16 

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1538 

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2371600 

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2427364 

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2.4 

Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 

Eighths    ! 
Tenths     ''       SQUARES 
of  Inches  | 

Feet,  Tnches 
and  Tenths 

Feet   Inches 


16 

16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
17 


10 
10* 


10* 

10| 
10f 
10* 

11 

11* 

m 

111 

11* 

lit 

111 

11* 

0 


1585 
1586 
1587 
1588 
1589 
1590 
1591 
1592 
1593 
1594 
1595 
1596 
1597 
1598 
1599 
1600 
1601 
1602 
1603 
1604 
1605 
1606 
1607 
1608 
1609 
1610 
1611 
1612 
1613 
1614 
1615 
1616 
1617 
1618 
1619 
1620 
1621 
1622 
1623 
1624 
1625 
1626 
1627 
1628 
1629 
1630 
1631 
1632 


•  2512225 
2515396 
2518569 
2521744 
2524921 
2528100 
2531281 
2534464 
2537649 
2540836 
2544025 
2547216 
2550409 
2553604 
2556801 
2560000 
2563201 
2566404 
2569609 
2572816 

.  2576025 
2579236 
2582449 
2585664 
2588881 
2592100 
2595321 
2598544 
2601769 
2604996 
2608225 
2611456 
2614689 
2617924 
2621161 
2624400 
2627641 
2630884 
2634129 
2637376 
2640625 
2643876 
2647129 
2650384 
2653641 
2656900 
2660161 
2663424 


Feet  Inches 

13  2.5 

13  2.6 
13 


13 

13 
13 

13 
13 
13 
13 
13 
13 
18 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 
13 


2.7 
2.8 
2.9 
3.0 
3.1 
3.2 
3.3 
3.4 
3.5 
3.6 
3.7 
3.8 
3.9 
4.0 
4.1 
4.2 
4.3 
4.4 
4.5 
4.6 
4.7 
4.8 
4.9 
5.0 
5.1 
5.2 
5.3 
5.4 
55 
5.6 
5.7 
5.8 
5.9 
6.0 
6.1 
6.2 
6.3 
6.4 
6.5 
6.6 
6.7 
6.8 
6.9 
7.0 
7.1 
7.2 


Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 

Eoliths 
>iii<l 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

17 

OJ 

1633 

26*6689 

13 

7.3 

17 

Oi 

1634 

2669956 

13 

7.4 

17 

Oj 

1635 

2673225 

13 

7.-r. 

17 

01 

1636 

2676496 

13 

7.6 

17 

01 

1637 

2679769 

13 

7.7 

17 

OJ 

1638 

2683044 

13 

7.8 

17 

01 

1639 

2686321 

13 

7.9 

17 

1 

1640 

2689600 

13 

8.0 

17 

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1641 

2692881 

13 

8.1 

17 

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1642 

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13 

8.2 

17 

if 

1643 

2699449 

13 

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17 

ij 

1644 

2702736 

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17 

if 

1645 

2706025 

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17 

if 

1646 

2709316 

18 

8.6 

17 

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1647 

2712609 

13 

8.7 

17 

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1648 

2715904 

13 

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17 

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1649 

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1650 

2722500 

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2729104 

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1653 

2732409 

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17 

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1654 

2735716 

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17 

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2739025 

13 

9.5 

17 

3 

1656 

2742336 

13 

9.6 

17 

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1657 

2745649 

13 

9.7 

17 

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1658 

2748964 

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9.8 

17 

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1659 

2752281 

13 

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17 

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1660 

2755600 

13 

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2758921 

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2768896 

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1665 

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1970 

2788900 

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179041 

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1679 

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6 

1080 

182X400 

14 

0.0 

Tables  of  Reductions  and  Squares 


Feet.  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches  j 

Feet 

Inches 

17 

6J  i   1681      2825761 

14 

0.1 

17 

6J     1682     2829124 

14 

0.2 

17 

6|     1683      2832489 

14 

0.3 

17 

6£     1684     2835856 

14 

0.4 

17 

6|     1685      2839225 

14 

0.5 

17 

6|     1686     2842596 

14 

0.6 

17 

6J     1687     28-15969 

14 

0.7 

17 

7     1688     2849344 

14 

0.8 

17 

7i     1689     2852721 

14 

0.9 

17 

1\     1690  !    2856100 

14 

1.0 

17 

7f  i   1691     2859481 

14 

1.1 

17 

ll     1692  i    2862864 

14 

1.2 

17 

7|  ;   1693     2866249 

14 

1.3 

17 

7|  :   1694     2869636 

14 

1.4 

17 

7i     1695     2873025 

14 

1.5 

17 

8 

1696      2876416 

14 

1.6 

17 

8J 

1697     2879809 

14 

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17 

8* 

1698     2883204 

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17 

8| 

1699 

2S86601 

14 

1.9 

17 

1700      2890000 

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1701 

2893401 

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17 

8| 

1702     2896804 

14 

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1703     2900209 

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2.3 

17 

9 

1704  i    2903616 

14 

2.4 

17 

91 

1705     2907025 

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Vk 

1706     2910436 

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26 

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91 

1707     2913849 

14 

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1708  ;    2917264 

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1709  i    2920681 

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2.9 

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91 

1710     2924100 

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3.0 

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91 

1711  !    2927521 

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10 

1712     2930944 

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WJ 

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3.3 

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lot 

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3.4 

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101 

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1728  1    21*85984 

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Tables  of  Reductions  and  Squares 


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Feet 
and 

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and 
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SQUARES 

Feet,  Inches 
and  Tenths 

of  Inches 

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Inches 

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Inches 

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fables  of  Reductions  and  Squares 


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Tables  of  Reductions  and  Squares 

I  II  III  IT 


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Eighths 

Tenths 
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SQUARES 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


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Tables  of  Reductions  and  Squares 

I  II  III  IV 


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3449 

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9.6 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.Inches 
and  Eighths 

EighthB 
and 
Tenths 
of  Inches 

SQUARES 

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01  j   3457     11950849 

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3459     11964681 

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3465     12006225 

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3466     12013156 

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3467     12020089 

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2.4 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
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Eighths 

Feet,  Inches 
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Te^hs     QUAKES 

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3505     12285025 

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3507  i   12299049 

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7.2 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
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Eighths 
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Tenths 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 
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Tables  of  Reductions  and  Squares 


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4.8 

Tables  of  Reductions  and  Squares 
i  ii  in  iv 


Feet.Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

i   SQUARES 

Feet.  Inches 
and  Tenths 

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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Feet,  Inches 
and  Eighths 

Eighths 
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2.4 

Tables  of  Reductions  and  Squares 


IV 


Eighths 

Feet,  Inches 
and  Tenths 

Feet.  Inches     and      QT>TTARH-« 
and  Eighths    Tenths 

of  incnes 

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Inches 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.  Indies 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

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Tables  of  Reductions  and  Squares 


Feet,  Inches 
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Tables  of  Reductions  and  Squares 


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Tables  of  Reductions  and  Squares 


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Tables  of  Reductions  and  Squares 


in 


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Tables  of  Reductions  and  Squares 


ii 


Feet,  Inches 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


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I  II  III  IV 


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Tables  of  Reductions  and  Squares 


Eighths 

Feet,  Inches 
and  Eighths 

and 

Tenths 

SQUARES 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
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50 

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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

1 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.  In 
and  Eig 

ches 
hths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

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ths 

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nches 

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2.4 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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Inches 

Feet 

Inches 

51 

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41 

2.5 

51 

61 

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61 

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51 

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61 

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7|     4955 

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7|     4958 

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41 

3.9 

51 

8     4960     24601600 

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41 

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41 

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7.2 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet.  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

52 

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41 

7.3 

52 

01 

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52 

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52 

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52 

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7.8 

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52 

1 

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41 

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52 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


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Tables  of  Reductions  and  Squares 

I  II  III  IV 


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Tables  of  Reductions  and  Squares 


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9.6 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

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117 


Tables  of  Reductions  and  Squares 


IV 


Eighths 

1 

Feet,  Inches 
and  Eighths 

and 
Tenths 

SQUARES 

,   Feet,  Inches 
and  Tenths 

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7.2 

Tables  of  Reductions  and  Squares 


Feet, 
and 

Eighths 

Inches     and 
Sighths  '  Tenths 
j  of  Inches 

SQUARES 

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aud  Tenths 

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Inches  I 

Feet 

Inches 

57 

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5473 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.  Inches 
and  Eighths 

Eighths  ! 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
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Tables  of  Reductions  and  Squares 


Eighths 

Feet,  lucbes 
and  Eighths 

xlnfhs     SQUARES 
of  Inches 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

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Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
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122 


Tables  of  Reductions  and  Squares 


Feet,  Inches 
ana  Eighths 

Eighths 

Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

•  59 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

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Tables  of  Reductions  and  Squares 


IV 


Feet,  ID 
and  Eig 

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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

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Feet,  Inches 
and  Tenths 

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Inches 

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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Feet 
and 

Inches 
Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
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Tables  of  Reductions  and  Squares 

I  IT  III  IT 


Feet,  Inches 
and  Eighths 

Eighths 

Feet,  Inches 
and  Tenths 

and 
Tenths 

SQUARES 

of  Inches 

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7.2 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eivhihs 
and 
Tenths 
of  Inches  i 

SQUARES 

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Tables  of  Reductions  and  Squares 

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I  II  III  IV 


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Tables  of  Reductions  and  Squares 

I  II  III  IT 


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Tables  of  Reductions  and  Squares 

I  II  III  IV 


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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Feet,  Inches 
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Tables  of  Reductions  and  Squares 


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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
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Tables  of  Reductions  and  Squares 


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9.6 

Tables  of  Reductions  and  Squares 

I  II  III  IT 


Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 
of  Inches 

SQUARES 

Feet.  Inches 
and  Tenths 

Feet 

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Inches 

76 

OJ     7297 

53246209 

60 

9.7 

76 

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7305 

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7306 

53377636 

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10.6 

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7307 

53392249 

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7308 

53406864 

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53582400 

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7322 

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7342 

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2.4 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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7346 

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53978409 

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7348     53993104 

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7349     54007801 

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7350     54022500 

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54051904 

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7354     54081316 

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7369 

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7370 

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Tables  of  Reductions  and  Squares 


Feet.  Inches 
and  Eighths 

1  Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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Tables  of  Reductions  and  Squares 


Feet.  Inches 
and  Eighths 

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and 
Tenths 
of  Inches 

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Tables  of  Reductions  and  Squares 


IV 


Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 
of  Inches 

SQUARES 

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and  Tenths 

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181 


Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

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and 
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2.4 

Tables  of  Reductions  and  Squares 


IV 


\  Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
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Feet 

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7632    58247424    63 

7.2 

Tables  of  Reductions  and  Squares 


\  Eighths 
Feet  Inches   !   and 
and  Eighths   !  Tenths 
of  Inches 

SQUARES 

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Inches 

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79 

6£     7633 

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63 

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79 

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0     7680     58982400     64 

0.0 

Tables  of  Reductions  and  Squares 


IV 


Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

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t  Teet 

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64 

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80 

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7727 

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7728 

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64 

4.8 

MB 


Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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9.6 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 

SQUARES 

Feet,  Inches 
and  Tenths 

of  Inches 

Feet 

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;   Feet 

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Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
Ttmhs     SQUARES 
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Feet,  inches 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

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Tables  of  Reductions  and  Squares 


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Tables  of  Reductions  and  Squares 


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I  II  III  IT 


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Feet,  Inches 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 

Feet,  Inches 
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Tables  of  Reductions  and  Squares 

I  II  III  iv 


Feet,  Inches 
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I  II  III  IV 


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Tables  of  Reductions  and  Squares 


Eighths  i 
Feet,  Inches     and 
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!  of  Inches 

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1-:: 


Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 
of  Inches 

SQUARES 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
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Tables  of  Reductions  and  Squares 


Feet,  Inches 
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Eighths 
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Tenths 
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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Eighths 

Feet 
and 

Inches 
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and 
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SQUARES     23'T 

Dches 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Feet.  Inches 
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TSuhs  1   SQUARES 
of  Inches 

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189 


Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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4.8 

Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

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i  >: 


Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 

Feet,  Inches 
and  Eighths 

and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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2.4 

Tables  of  Reductions  and  Squares 

I  II  III 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

saar 

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in 


Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
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0.0 

Tables  of  Reductions  and  Squares 


in 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

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4.8 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inrhes 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
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Tables  of  Reductions  and  Squares 


Feet,  Inches 
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Eighths 
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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Eighths 
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1  of  Inches 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Foet,  Inches 
and  Eighths 

Eighths 

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of  Inches  | 

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Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 


Feet 
98 
98 
98 
98 
98 
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0* 
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and 

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of  Inches 


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88529281 
88548100 
88566921 
88585744 
88604569 
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88642225 
88661056 


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78 
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8.5 

8.6 

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8.8 

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9.0 

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9.3 

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9.5 

9.6 


Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 

Feet,  Inches     and 
and  Eighths    Tenths 

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Tables  of  Reductions  and  Squares 


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Tables  of  Reductions  and  Squares 

I  II  III  IT 


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Tables  of  Reductions  and  Squares 


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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Feet,  Inches 
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9.6 

Tables  of  Reductions  and  Squares 


in 


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Feet,  Inches     and 
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2.4 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
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Tenths 
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7.2 

Tables  of  Reductions  and  Squares 

I  II  III  iv 


Eighths 

Feet.  Inches 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

qoTTAR-pq     Feet,  Inches 
SQUARES   .   &nd  Tenthg 

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4.8 

Tables  of  Reductions  and  Squares 


Feet,  Inches  i 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

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and  Tenths 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 

Tenths 
of  Inches 

SQUARES 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

I 

^QUARKS;     Feet,  Inches 
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0.0 

Tables  of  Reductions  and  Squares 


IV 


Eighths 

Feet,  Inches  and 

and  Eighths          Tenths 
of  Inches 


SQUARES 


Feet  Inches 
105  OJ 
105  0} 
105  Of 
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10081 
10082 


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5i 
6 


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Feet,  Inches 
and  Tenths 


Feet  Inches 
84  0.1 
84  0.2 
84  0.3 
0.4 
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-I 


1.0 

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.2 

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1.8 

19 

2.0 

2.1 

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2.8 
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3.2 
3.3 

3.5 
3.6 
3.7 

3.8 

4.0 

4.2 
4.3 
4.4 

4.7 
4.8 


H6 


Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 
Feet,  Inches     and      SQTTARFS 
and  Eighths    Tenths     ««lUAKJib 
of  Inches  i 

Feet,  Inches 
I   and  Tenths 

Feet 

Inches 

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10132 

102657424 

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10133 

102677689 

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102697956 

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10138  1  102779044    84 

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10139    102799321     84 

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10140    102819600     84 

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10141    102839881     84 

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10143    102880449     84 

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10147    102961609    84 

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10148 

102981904     84 

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10150 

103022500 

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9.6 

Tables  of  Reductions  and  Squares 


Eighths  ! 

Feet, 
and] 

Inches 

Sightns 

and 
Tenths 

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10200 

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10219 

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10220 

104448400 

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104468841 

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10222 

104489284 

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106 

5£ 

10223 

104509729 

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10224 

104530176 

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2.4 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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Inches 

Feet 

Inches 

106 

6£ 

10225    104550625     85 

2.5 

106 

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10226  ,  104571076     85 

2.6 

106 

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10227  ,  104591529     85 

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6J    10228  !  104611984  '   85 

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10232 

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10234    104734756 

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10235    104755225 

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10236    104775696 

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10240 

104857600     85 

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10243    104919049 

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10244  ;  104939536     85 

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4.5 

106 

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4.6 

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10247    105001009     85 

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9 

10248    105021504     85 

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105042001 

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10256  |  105185536 

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10257  i  105206049 

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10258    105226564 

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7.2 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.Inches 
and  Eighths 

Eighths 
and 
Tenths 
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SQUARES 

Feet,  Inches 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
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Tables  of  R<  Auctions  and  Squares 

I  II  III  IV 


Eighths 
Feet,  Inches     and 
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SQUARES 

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Feet,  Inches 
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Inches 

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Tables  of  Reductions  and  Squares 


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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
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Eighths 
and 
Tenths 
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Tables  of  Reductions  and  Squares 

I  II  III  IT 


Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 
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Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 

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and 
Tenths 
of  Inches 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
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qoiTARF<;     Feet,  Inches 
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Tables  of  Reductions  and  Squares 


Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 
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SQUARES 

and  'Tenths 

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227 


Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
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Tables  of  Reductions  and  Squares 

III  IV 


Eighths 

Feet, 
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Inches     and 
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116640000 

0.0 

Tables  of  Reductions  and  Squares 

I  IE  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

112 

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10801  |  116661601 

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4.8 

Tables  of  Reductions  and  Squares 


IV 


Eighths 
Feet.  Inches     and 
and  Eighths    Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

113 

0£    10849    117700801 

90 

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64 

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90 

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90 

:-..; 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 
Feet,  Inches   ;   and 
and  Eighths     Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

113 

6£    10897 

118744609 

90 

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113 

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91 

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113 

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10943 

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114 

0 

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2.4 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

114 

OJ    10945 

119793025 

91 

2.5 

114 

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91 

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7.2 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 
Feet  Inches     and 
and  Eighths    Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

114 

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0.0 

Tables  of  Reductions  and  Squares 


IV 


Ft.-t.-t,  Inches 
and  Eighths 

Eighths 
T&tL     SQUARES 
of  Inches 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

115 

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92 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


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Tables  of  Reductions  and  Squares 

I  II  III  IV 


1  Eighths  ' 
Feet,  Inches     and*     SOTTARFS 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
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Eighths 
and 
Tenths 
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Tables  of  Reductions  and  Squares 


IV 


Eighths 

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iS?h1    Tenths     ^QUAKES 
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Tables  of  Reductions  and  Squares 


Eighths 
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Tables  of  Reductions  and  Squares 


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11.3 

118 

8}  i  11394    129823236  i   94 

11.4 

118 

8|    11395    129846025  i   94 

11.5 

118 

8J  i  11396    129868816     94 

11.6 

118 

8|    11397    129891609     94 

11.7 

118 

8J    11398    129914404     94 

11.8 

118 

gf 

11399    129937201     94 

11.9 

118 

9 

11400 

129960000     95 

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118 

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11401 

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0.1 

118 

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11402 

130005604     95 

0.2 

118 

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11403 

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0.3 

118 

9J  !  11404    130051216     95 

0.4 

118 

9|  !  11405    130074025  i   95 

0.5 

118 

9|  j  11406  1  130096836  j   95 

0.6 

118 

9|    11407  i  130119649     95 

0.7 

118 

10     11408  i  130142464     95 

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118 

101    H409  !  130165281     95 

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118 

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111    11417 

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lit    H418 

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11419 

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11422 

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118 

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119 

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2.4 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 

1 

Feet,  Inches 
and  Eighths 

and 
Tenths 

SQUARES 

Feet,  Inches 
and  Tenths 

of  Inches 

i 

Feet 

Inches 

Feet 

Inches 

119 

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11425 

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95 

2.5 

119 

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11426 

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11427 

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11428 

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11430 

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11431 

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11432 

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11433    130713489 

95 

3.3 

119 

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11434    130736356 

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11435  I  130759225  \ 

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11437    130804969 

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11439 

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119 

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11440    130873600 

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119 

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119 

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11442  |  130919364 

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119 

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11443    130942249 

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4.3 

119 

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4.4 

119 

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11445  !  130988025 

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4.5 

119 

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11446  ';  131010916 

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4.6 

119 

2i 

11447  I  131033809 

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4.7 

119 

3 

11448    131056704 

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4.8 

119 

34 

11449    131079601 

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119 

31 

11450    131102500 

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6.0 

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11451    131125401 

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114£4  1  131194116 

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11455    131217025 

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5.5 

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11458    131285764 

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11459  ;  131308681 

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119 

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11460    131331600 

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119 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 

Feet,  Inches 
and  Tenths 

Feet.  Inches 
and  Eighths 

and 
Tenths 

SQUARES 

1  oi  inches 

Feet 

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I   Feet   Inches 

119 

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11473 

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0.0 

Tables  of  Reductions  and  Squares 


Eighths 

Feet  .Inches 
and  Eighths 

and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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Inches 

1 

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120 

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4.8 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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120 

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11577    134026929 

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Tables  of  Reductions  and  Squares 


Eighths 

Feet.  Inches 
and  Eighths 

and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inchea 

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2.4 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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Inches 

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7.2 

Tables  of  Reductions  and  Squares 


Eighths 

Feet.Tnches 
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and 

Tenths 
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SQUARES 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Foet,  Inches 
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Tenths 
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4.8 

Tables  of  Reductions  and  Squares 


Feet.  Inches 
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Eighths 
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Tenths 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
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Tenths 
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Tables  of  Reductions  and  Squares 


IV 


Feet.  Inches 
and  Eighths 

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Tables  of  Reductions  and  Squares 


Eighths 

Feet,  Inches 
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Inches     and 
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Tables  of  Reductions  and  Squares 
>  ii  in 


Feet,  Inches 
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100 

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125 

2J 

12017 

144408289 

100 

1.7 

125 

21 

12018 

144432324 

,  100 

1.8 

125 

2f 

12019 

1444.56361 

100 

1.9 

125 

2* 

12020 

144480400 

100 

2.0 

125 

gf 

12021 

144504441 

100 

2.1 

125 

2J 

12022 

144528484 

100 

2.2 

125 

21 

12023 

144552529 

100 

2.3 

125 

3 

12024 

144576576 

100 

2.4 

125 

3J 

12025 

144600625 

;   100 

2.5 

125 

S| 

12026 

144624676 

100 

2.6 

125 

3| 

12027 

144648729 

100 

2.7 

125 

3* 

12028 

144672784 

100 

2.8 

125 

3| 

12029 

144696841 

100 

•_'.'.* 

125 

3| 

12030 

144720'JOO 

100 

3.0 

125 

3J 

12031 

144744961 

100 

3.1 

125 

4 

12032 

144769024 

100 

3.2 

125 

4J 

12033 

144793089 

100 

3.3 

1  •!'> 

4J 

12034 

144817156 

100 

3.4 

125 

4| 

12035 

144841225 

100 

3.5 

125 

4* 

12036 

144865296 

100 

3.6 

125 

4| 

12037 

144889369 

100 

3.7 

125 

4? 

12038 

144913444 

100 

3.8 

125 

4J 

12039 

144937521 

100 

1.9 

125 

5 

12040 

144961600 

100 

4.0 

125 

5£  • 

12041 

144985681 

100 

1.1 

125 

5^ 

12042 

145009764 

100 

4.2 

125 

5| 

12043 

1  i:.0.'!3849 

100 

4.3 

12-. 

6j 

12044 

1  450:.::  •::.; 

100 

4.4 

125 

5| 

12045 

145082025 

100 

4.:. 

125 

5J 

12046 

145106116 

100 

4.6 

125 

5£ 

12047 

M5  130209 

100 

4.7 

125 

6 

12048 

145154304 

100 

4.8 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 

Feet,  Inches 
and  Tenths 

Feet,  Inches 
and  Eighths 

and 
j  Tenths 

SQUARES 

of  Inches 

Feet 

Inches 

Feet 

Inches 

125 

6J 

12049 

145178401 

100 

4.9 

125 

6} 

12050 

145202500 

100 

5.0 

125 

6| 

12051 

145226601 

100 

5.1 

125 

ej 

12052 

145250704 

100 

5.2 

125 

6| 

12053 

145274809 

100 

5.3 

125 

12054 

145298916 

100 

5.4 

125 

61 

12055 

145323025 

100 

5.5 

125 

7 

12056 

145347136 

100 

5.6 

125 

7J 

12057 

145371249 

100 

5.7 

125 

7i 

12058 

145395364 

100 

5.8 

125 

7| 

12059 

145419481 

100 

5.9 

125 

n 

12060 

145443600  j  100 

6.0 

125 

7| 

12061 

145467721    100 

6.1 

125 

7| 

12062 

145491844    100 

6.2 

125 

71 

12063 

145515969    100 

6.3 

125 

8 

12064 

145540096    100 

6.4 

125 

8} 

12065 

145564225    100 

6.5 

125 

8} 

12066 

145588356    100 

6.6 

125 

81 

12067 

145612489    100 

6.7 

125 

12068 

145636624    100 

6.8 

125 

8| 

12069 

145660761    100 

6.9 

125 

8| 

12070 

145684900    100 

7.0 

125 

8  1 

12071 

145709041 

100 

7.1 

125 

9 

•12072 

145733184 

100 

7.2 

125 

9J 

12073 

145757329 

100 

7.3 

125 

9} 

12074 

145781476 

100 

7.4 

125 

9| 

12075 

145805625  j  100 

7.5 

125 

9| 

12076 

145829776  !  100 

7.6 

125 

9| 

12077 

145853929    100 

7.7 

125 

9| 

12078 

145878084    100 

7.8 

125 

91 

12079 

145902241  I  100 

7.9 

125 

10 

12080 

145926400    100 

8.0 

125 

m 

12081 

145950561 

100 

8.1 

125 

10} 

12082 

145974724 

100 

8.2 

125 

10| 

12083 

145998889    100 

83 

125 

10.V 

12084 

146023056    100 

8.4 

125 

10  1 

12085 

146047225    100 

8.5 

125 

io| 

12086 

146071396    100 

8.6 

125 

io| 

12087 

146095569    100 

8.7 

125 

11 

12088 

146119744    100 

8.8 

125 

HI 

12089 

146143921  |-  100 

8.9 

125 

11} 

12090 

146168100 

100 

9.0 

125 

ill 

12091 

146192281 

100 

9.1 

125 

Hi 

12092 

146216464 

100 

9.2 

125 

nf 

12093 

146240649 

100 

9.3 

125 

ill 

12094 

146264836 

100 

9.4 

125 

Uf 

12095 

146289025 

100 

9.5 

126 

o 

12096 

146313216  !  100 

9.6 

Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

j 
Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

126 

01 

12097    146337409 

100 

9.7 

126 

OJ 

12098    146361604    100 

9.8 

126 

Of 

12099    146385801  j  100 

9.9 

126 

0} 

12100    146410000    100 

10.0 

126 

Of    12101    146434201    100 

10.1 

126 

Of  !  12102  I  146458404    100 

10.2 

126 

01    12103  |  146482609    100 

10.3 

126 

1     12104    146506816    100 

10.4 

126 

U  i  12105  ;  146531025    100 

10.5 

126 

H  !  12106    146555236    100 

10.6 

126 

11^  j  12107  1  146579449  j  100 

10.7 

126 

1J*   12108  i  146603664    100 

10.8 

126 

If  ;  12109 

146627881    100 

10.9 

126 

If    12110 

146652100  !  100 

11.0 

126 

1J  i  12111  |  146676321  |  100 

11.1 

126 

2   j  12112  i  146700544  i  100 

11.2 

126 

21  i  12113    146724769  \  100 

11.3 

126 

2J-    12114  i  146748996    100 

11.-4 

126 

2|    12115    146773225    100 

11.5 

126 

2J    12116  i  146797456    100 

11.6 

126 

2|    12117    146821689 

100 

11.7 

126 

2J    12118    146845924 

100 

11.8 

126 

21    12119    146870161    100 

11.9 

126 

3     12120    146894400 

101 

0.0 

126 

3£    12121  j  146918641 

101 

0.1 

126 

3£    12122    146942884    101 

0.2 

126 

3|    12123    146967129  !  .101 

0.3 

126 

3£    12124 

146991376 

101 

0.4 

126 

3|    12125 

147015625 

101 

0.5 

126 

3|    12126    147039876    101 

0.6 

126 

3£    12127  |  147064129  !  101 

0.7 

126 

4   j  12128    147088384 

101 

0.8 

126 

4£    12129 

147112641 

101 

0.9 

126 

4J    12130 

147136900 

101 

1.0 

126 

4|    12131 

147161161 

101 

1.1 

126 

4* 

12132 

147185424 

101 

1.2 

126 

41 

12133 

147209689 

101 

1.3 

126 

4J 

12134 

147233956 

101 

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126 

4£ 

12135 

147258225 

101 

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126 

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12136 

147282496 

101 

1.6 

126 

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12137 

147306769 

101 

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126 

§* 

12138 

147331044 

101 

1.8 

126 

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12139 

147355321 

101 

1.9 

126 

5* 

12140 

147379600 

101 

2.0 

126 

5| 

12141 

147403881    101 

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12142 

147428164    101 

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126 

5£ 

12143 

147452449    101 

2.3 

126 

6     12144 

147476736    101 

2.4 

107 


Tables  of  Reductions  and  Squares 


Feet, 
and] 

Inches 
Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

126 

6J 

12145 

147501025 

101 

2.5 

126 

6£ 

12146 

147525316 

101 

2.6 

126 

6|    12147 

147549609 

101 

2.7 

126 

6£    12148 

147573904 

101 

2.8 

126 

6|    12149 

147598201 

101 

2.9 

126 

6|    12150 

147622500 

101 

3.0 

126 

6£    12151 

147646801 

101 

3.1 

126 

7     12152 

147671104 

101 

3.2 

126 

7i    12153 

147695409 

101 

3.3 

126 

7£    12154    147719716 

101 

3.4 

126 

7|    12155    147744025 

101 

3.5 

126 

7*    12156    147768336 

101 

3.6 

126 

7|    12157 

147792649 

101 

3.7 

126 

7|    12158 

147816964 

101 

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126 

7J    12159 

147841281 

101 

3.9 

126 

8     12160 

147865600 

101 

4.0 

126 

8£    12161 

147889921 

101 

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sl    12162 

147914244 

101 

4.2 

126 

8f    12163 

147938569 

101 

4.3 

126 

8£    12164 

147962896 

101 

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126 

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12165 

147987225 

101 

4.5 

126 

8|    12166 

148011556 

101 

4.6 

126 

8£    12167 

148035889    101 

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126 

9     12168 

148060224 

101 

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126 

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12169 

148084561 

101 

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126 

9i 

12170 

148108900 

101 

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126 

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12171 

148133241 

101 

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126 

9* 

12172 

148157584 

101 

5.2 

126 

9| 

12173 

148181929 

101 

5.3 

126 

9| 

12174 

148206276    101 

5.4 

126 

91 

12175    148230625  1  101 

5.5 

126 

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148254976    101 

5.6 

126 

10* 

12177 

148279329 

101 

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126 

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12178 

148303684 

101 

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126 

10f 

12179 

148328041 

101 

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126 

10* 

12180    148352400 

101 

6.0 

126 

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12181    148376761 

101 

6.1 

126 

lOf  !  12182    148401124    101 

6.2 

126 

10|  !  12183    148425489    101 

6.3 

126 

11     12184 

148449856    101 

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126 

11* 

12185 

148474225    101 

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126 

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12186 

148498596    101 

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126 

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12187 

148522969    101 

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126 

11J 

12188 

148547344    101 

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126 

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12189 

148571721  ;  101 

6.9 

126 

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12190 

148596100    101 

7.0 

126 

HI 

12191 

148620481 

101 

7.1 

127 

0 

12192 

148644864 

101 

7.2 

Tables  of  Reductions  and  Squares 


Eighths 

Feet,  Inches     "and 
and  Eighths   ,  Tenths 

SQUARES     FCdtT 

[nches 

of  Inches 

Feet 

Inches  •                     Feet 

Inchea 

127 

OJ    12193    148669249    101 

7.3 

127 

01 

12194  ,  148693636    101 

7.4 

127 

01 

12195    148718025    101 

7.5 

127 

0} 

12196.   148742416    101 

7.6 

127 

0| 

12197  |  148766809    101 

7.7 

127 

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12198    148791204    101 

7.8 

127 

OJ 

12199    148815601    101 

7.9 

127 

1 

12200    148840000    101 

8.0 

127 

1J    12201    148864401    101 

8.1 

127 

1J-    12202    148888804  !  101 

8.2 

127 

1|  ;  12203    148913209    101 

8.3 

127 

1J    12204    148937616    101 

8.4 

127 

H 

12205    148962025 

101 

8.5 

127 

If 

12206    148986436 

101 

8.6 

127 

H    12207    149010849    101 

8.7 

127 

2 

12208    149035264  :  101 

8.8 

127 

2J    12209    149059681    101 

8.9 

127 

2J    12210  [  149084100  j  101 

9.0 

127 

2|  j  12211  '  149108521    1<U 

9.1 

127 

2}    12212  I  149132944    101 

9.2 

127 

2|    12213  I  149157369    101 

9.3 

127 

2J  {  12214  j  149181796    101 

9.4 

127 

2|    12215    149206225    101 

9.5 

127 

3     12216    149230656 

101 

l>.6 

127 

3J    12217 

1492.55089 

101 

9.7 

127 

3}    12218    149279524 

101 

9.8 

127 

8| 

12219    149303961 

101 

9.9 

127 

3J 

12220  ;  149328400  i  101 

10.0 

127 

3|    12221    149352841    101 

10.1 

127 

3|    12222    149377284 

101 

10.2 

127 

31 

12223 

149401729    101 

10.3 

127 

4 

12224 

149426176    101 

10.4 

127 

41    1222-5 

149450625 

101 

10.5 

127 

4*  1  12226 

149475076    101 

10.6 

127 

43 

12227 

149499529    101 

10.7 

127 

4* 

12228 

149523984    101 

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127 

4$ 

12229 

149-548441 

101 

10.9 

127 

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12230 

149572900 

101 

11.0 

127 

41 

12231 

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101 

11.1 

1*7 

5 

12232 

149621824 

101 

11.2 

127 

5| 

12233 

149646289 

101 

11.3 

127 

5} 

12234 

149670756 

101 

11.4 

127 

5| 

12235 

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101 

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127 

5J 

12236 

149719696 

101 

11.0 

127 

5| 

12237 

149744169 

101 

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127 

5J 

12238 

149768644 

101 

11.8 

127 

51 

(2289 

141)793121 

101 

11.'.' 

127 

6 

12240 

149817600 

102 

0.0 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

127 

6£ 

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149842081 

102 

0.1 

127 

6} 

12242 

149866564 

1-02 

0.2 

127 

6| 

12243 

149891049 

102 

0.3 

127 

8i 

12244 

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102 

0.4 

127 

6f 

12245 

149940025 

102 

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127 

61 

12246 

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102 

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127 

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12250 

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12252 

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7| 

12253 

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102 

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127 

n 

12254 

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102 

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127 

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12255 

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127 

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12259 

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127 

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12260 

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127 

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12261 

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127 

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12262 

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12263 

150381169 

102 

2.3 

127 

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12264 

150405696 

102 

2.4 

127 

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12265 

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127 

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12266 

150454756 

102 

2.6 

127 

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12267 

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102 

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127 

9* 

12268 

150503824 

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127 

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12269 

150528361 

102 

2.9 

127 

91 

12270 

150552900 

102 

3.0 

127 

9£ 

12271 

150577441 

102 

3.1 

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10 

12272 

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102 

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10J 

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102 

3.3 

127 

10* 

12274 

150651076 

102 

3.4 

127 

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127 

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Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

128 

OJ  j  12289 

151019521 

102 

4.9 

128 

o* 

12290 

151044100 

102 

5.0 

128 

0| 

12291 

151068681    102 

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128 

0* 

12292    151093264  !  102 

5.2 

128 

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12293    151117849    102 

5.3 

128 

0} 

'  12294    151142436    102 

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128 

0£ 

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128 

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12297 

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128 

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12298    151240804    102 

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128 

if 

12299    151265401    102 

5.9 

128 

1J 

12300 

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6.0 

128 

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12301    151314601  ;  102 

6.1 

128 

U 

12302    151339204    102 

6.2 

128 

U 

12303    151363809    102 

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2 

12304    151388416    102 

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12320    151782400 

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12322 

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12324 

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128 

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12328 

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12333 

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9.3 

128 

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12334 

1521  27  .V,r. 

102 

9.4 

128 

5J 

12335 

1.  -.21-  -.2225    102 

9.6 

128 

6 

12336 

152176896    102 

9.6 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

128 

g£ 

12337 

152201569 

102 

9.7 

128 

6i 

12338    152226244 

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128 

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12339    152250921  i  102 

9.9 

128 

6* 

12340    152275600    102 

10.0 

128 

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12341    152300281.   102 

10.1 

128 

61 

12342    152324964    102 

10.2 

128 

12343 

152349649    102 

10.3 

128 

7 

12344 

152374336    102 

10.4 

128 

7j 

12345 

152399025    102 

10.5 

128 

7j 

12346 

152423716 

102 

10.6 

128 

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12347 

152448409 

102 

10.7 

128 

7£    12348 

152473104    102 

10.8 

128 

1\    12349 

152497801    102 

10.9 

128 

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11.0 

128 

7|    13351 

152547201    102 

11.1 

128 

8 

12352 

152571904    102 

11.2 

128 

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12353 

152596609    102 

11.3 

128 

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12354 

152621316 

102 

11.4 

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12355 

152646025 

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11.5 

128 

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12356 

152670736 

102 

11.6 

128 

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12357 

152695449 

102 

11.7 

128 

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12358 

152720164 

102 

11.8 

128 

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12359 

152744881 

102 

11.9 

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12360 

152769600 

103 

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12361 

152794321 

103 

0.1 

128 

9i 

12362 

152819044 

103 

0.2 

128 

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12363 

152843769 

103 

0.3 

128 

9J 

12364 

152868496 

103 

0.4 

128 

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12365 

152893225 

103 

0.5 

128 

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12366    152917956 

103 

0.6 

128 

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12367    152942689  ;  103 

0.7 

128 

10 

12368 

152967424    103 

0.8 

128 

10J 

12369 

152992161    103 

0.9 

128 

lot 

12370 

153016900 

103 

1.0 

128 

10| 

12371 

153041641 

103 

1.1 

128 

10J 

12372 

153066384 

103 

1.2 

128 

10f 

12373 

153091129 

103 

1.3 

128 

10* 

12374 

153115876 

103 

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128 

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12375 

153140625 

103 

1.5 

128 

11 

12376 

153165376  {  103 

1.6 

128 

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12377 

153190129 

103 

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128 

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12378 

153214884 

103 

1.8 

128 

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12379 

153239641 

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12380 

153264400 

103 

2.0 

128 

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12381 

153289161 

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111 

12382    153313924 

103 

2.2 

128 

111    12383    153338689 

103 

23 

129 

0     12384  '  1533G3456 

103 

2.4 

Tables  of  Reductions  and  Squares 


in 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

129 

OJ 

12385 

153388225 

103 

2.5 

129 

0* 

12386 

153412996 

103 

2.6 

129 

<>. 

12387 

153437769 

103 

2.7 

129 

OJ    12388 

153462544 

103 

2.8 

129 

0|    12389 

153487321    103 

2.9 

129 

Of 

12390 

153512100    103 

3.0 

129 

o* 

12391 

153536881    103 

3.1 

129 

1     12392 

153561664    103 

3.2 

129 

1J  i  12393 

!  153586449    103 

3.3 

129 

IJ    12394 

153611236  '  103 

3.4 

129 

If    12395 

153636025    103 

3.5 

129 

11 

12396 

153660816    103 

3.6 

129 

If 

12397 

153685609    103 

3.7 

129 

It 

12398 

153710404 

103 

3.8 

129 

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12399 

153735201 

103 

3.9 

129 

2 

12400 

153760000 

103 

4.0 

129 

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12401 

153784801 

103 

4.1 

129 

2* 

12402 

153809604 

103 

4.2 

129 

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12403 

153834409 

103 

4.3 

129 

2* 

12404 

153859216 

103 

4.4 

129 

2| 

12405 

153884025 

103 

4.5 

129 

2| 

12406 

153908836    103 

4.6 

129 

31 

12407 

153933649  1  103 

4.7 

129 

3 

12408 

153958464    103 

4.8 

129 

3* 

12409 

153983281  |  103 

4.9 

129 

3* 

12410 

154008100    103 

5.0 

129 

31 

12411 

154032921    103 

5.1 

129 

3J 

12412 

154057744    103 

5.2 

129 

31 

12413 

154082569    103 

5.3 

129 

3| 

12414 

154107396    103 

5.4 

129 

8} 

12415 

154132225    103 

5.5 

129 

4 

12416 

154157056    103 

5.6 

129 

4J- 

12417 

154181889    103 

5.7 

129 

4* 

12418 

154206724    103 

5.8 

129 

4f 

12419 

154231561 

103 

5.9 

129 

4* 

12420 

154256400 

103 

6.0 

129 

4f 

12421 

154281241 

103 

6.1 

129 

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12422 

154306084 

103 

6.2 

129 

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12423 

154330929 

103 

6.3 

129 

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12424 

154355776 

103 

6.4 

129 

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12425 

154380625 

103 

6.5 

129 

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12426 

154405476 

103 

6.6 

129 

5|    12427 

154430329    !<•:; 

6.7 

129 

5J  j  12428 

1544.55184 

103 

6.8 

129 

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154480041 

103 

6.9 

129 

5|    12430 

154504900    103 

7.0 

129 

5J 

12431 

K.I.VJ9761  |  103 

7.1 

129 

6 

12432 

154554624  i  103 

7.2 

263 


Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

129 

6J 

12433 

154579489 

103 

7.3 

129 

6* 

12434 

154604356 

103 

7.4 

129 

6| 

12435 

154629225 

103 

7.5 

129 

6* 

12436    154654096    103 

7.6 

129 

6| 

12437    154678969    103 

7.7 

129 

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12438    154703844 

103 

7.8 

129 

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12439    154728721 

103 

7.9 

129 

7 

12440  1  154753600 

103 

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129 

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12441 

154778481 

103 

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129 

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12442 

154803364 

103 

8.2 

129 

71 

12443 

154828249 

103 

8.3 

129 

7* 

12444 

154853136 

103 

8.4 

129 

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12445 

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8.5 

129 

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12446 

154902916 

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8.6 

129 

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12447 

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103 

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129 

8 

12448 

154952704 

103 

8.8 

129 

8J 

12449 

154977601 

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8.9 

129 

8J 

12450    155002500 

103 

9,0 

129 

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12451    155027401 

103 

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129 

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12452 

155052304 

103 

9.2 

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12453 

155077209 

103 

9.3 

129 

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12454 

155102116 

103 

9.4 

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155127025 

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9.5 

129 

9 

12456 

155151936  |  103 

9.6 

129 

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12457 

155176849 

103 

9.7 

129 

at 

12458 

155201764    103 

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129 

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12459 

155226681    103 

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129 

9* 

12460 

155251600    103 

10.0 

129 

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12461 

155276521    103 

10.1 

129 

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12462 

155301444 

103 

10.2 

129 

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12463 

155326369    103 

10.3 

129 

10 

12464 

155351296    103 

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129 

191 

12465 

155376225 

103 

10.5 

129 

10* 

12466 

155401156 

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10.6 

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12467    155426089 

103 

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12468    155451024 

103 

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12469    155475961 

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12477  j  155675529 

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11.7 

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111 

12478  !  155700484 

103 

11.8 

129 

113 

12479    155725441 

103 

11.9 

130 

0 

12480  i  155750400 

104 

0.0 

Tables  of  Reductions  and  Squares 

I  II  III  IT 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 

SQUARES 

Feet,  Inches 
and  Tenths 

of  Inches 

Feet 

Inches 

Feet 

Inches 

130 

OJ  , 

12481 

155775361 

104 

0.1 

130 

o* 

12482 

155800324 

104 

0.2 

130 

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12483 

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104 

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104 

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130 

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12486 

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104 

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12487 

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130 

u 

12489 

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12490 

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12491 

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12492 

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12493 

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104 

1.3 

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H 

12494 

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12495 

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104 

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130 

2 

12490 

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12497 

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21 

12498 

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104 

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130 

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12499 

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104 

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130 

2* 

12500 

156250000 

104 

2.0 

130 

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12501 

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104 

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12502 

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104 

2.2 

130 

2* 

12503 

156325009 

104 

2.3 

130 

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12504 

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104 

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130 

3J 

12505 

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130 

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12506 

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104 

2.6 

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104 

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12508 

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12510 

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12511 

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12514 

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104 

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104 

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12516 

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104 

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12517 

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104 

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130 

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12518 

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104 

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104 

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130 

5 

12520 

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104 

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130 

5J 

12521 

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104 

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130 

N 

12522 

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104 

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12523 

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104 

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130 

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12524 

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104 

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12525 

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104 

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130 

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12526 

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104 

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130 

5J 

12527 

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104 

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6 

12528 

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104 

48 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 

-  i 

and 
Tenths 

QOTTARTJX     FeeUInches 
SQUAREb     and  Tenths 

of  Inches 

Feet 

Inches  i 

Feet 

Inches 

130 

&l     12529 

156975841    104 

4.9 

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12533 

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12534 

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130 

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12535 

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130 

7     12536 

157151296    104 

5.6 

130 

7J  I  12537  , 

157176369    104 

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130 

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5.8 

130 

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12539 

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130 

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12540 

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6.0 

130 

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12541 

157276681 

104 

6.1 

130 

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12542 

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104 

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157326849    104 

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12544  , 

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130 

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12548 

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130 

81    12551 

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104 

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130 

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130 

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9£    12556 

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104 

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104 

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104 

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104 

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111    12575  j 

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9.6 

Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

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Inches 

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104 

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2.4 

Tables  of  Reductions  and  Squares 


Eighths 
Feet,  Inches     and 
and  Eighths  |  Tenths 
j  of  Inches 

SQUARES 

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and  Tenths 

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Inches  i 

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7.2 

Tables  of  Reductions  and  Squares 


Eighths 

Feet.  Inches 
and  Eighths 

and 
Tenths 
•  of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

132 

oj- 

12673    160604929 

105 

7.3 

132 

o* 

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105 

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105 

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105 

8.2 

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12683  j  160858489 

105 

8.3 

132 

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12684  1  160883856 

105 

8.4 

132 

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12685  !  160909225 

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8.5 

132 

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12686    160934596 

105 

8.6 

132 

If 

12687    160959969 

105 

8.7 

132 

2 

12688  i  160985344    105 

8.8 

132 

2i 

12689    161010721 

105 

8.9 

132 

2* 

12690    161036100 

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9.0 

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9.4 

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3J 

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161213809 

105 

9.7 

132 

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105 

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12699 

161264601 

105 

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12702 

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10.6 

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12710 

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12712    161594944    105 

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269 


Tables  of  Reductions  and  Squares 


Feet 
and 

,  Inches 
Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet 
and 

Inches 
Tenths 

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Inches 

Feet 

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6f 

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12736 

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2.7 

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4.8 

Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

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4.9 

133 

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5.4 

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12775    163200625    106 

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5.6 

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5.8 

133 

11 

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5.9 

133 

li 

12780  j  163328400 

106 

6.0 

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1|    12781    163353961 

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11  i  12783    163405089 

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6.3 

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2     12784  1  163430656 

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6.4 

133 

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106 

6.5 

133 

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6.6 

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5£    12815    164224225    106 

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6     12816    164249866    106 

9.6 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
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Feet 

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11    12831 

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8     12832 

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11.2 

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2.4 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Bgttttu 

and 
Tenths 
of  Inches 

SQUARES 

Feet.  Inches 
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7.2 

Tables  of  Reductions  and  Squares 


Feet  Inches 
and  Eighths 

Eighths 
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Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
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167909764    107 

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167961600    108 

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Tables  of  Reductions  and  Squares 


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Feet,  Inches 
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Tenths 
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SQUARES 

Feet,  Inches 
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Feet 

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135 

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Tables  of  Reductions  and  Squares 


Feet,  Inches 
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13036 

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13037 

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Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
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Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
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Feet 

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1704&5249 

108 

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13059    170537481 

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13073  i  170903329 

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Tables  of  Reductions  and  Squares 


Feet,  Inches 
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Eighths 
and 
Tenths 
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SQUARES 

Feet,  Inches 
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7.2 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


1  Eighths 
Feet,  Inches     and 
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of  Inches 

SQUARES 

Feet,  Inches 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
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Tenths 
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176145984 

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138 

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9.6 

m 


Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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71 

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2.4 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

139 

OJ 

13345 

178089025 

111 

2.5 

139 

o* 

13346 

178115716 

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2.6 

139 

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13347 

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139 

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13348 

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13350 

178222500 

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139 

0£  !  13351 

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1     13352 

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139 

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2     13360 

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13364 

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7.0 

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51    13391 

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6     13392 

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7.2 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

.Inches 

139 

6J 

13393 

179372449 

111 

7.3 

139 

6J    13394 

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7.4 

139 

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13395 

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13396 

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7     13400 

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7£    13401 

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8.4 

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7|  i  13405 

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8.5 

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8.6 

139 

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8.7 

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8     13408 

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13425    180230625 

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0.0 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

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140 

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112 

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140 

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13442 

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112 

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13453 

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1.3 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

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13490    181980100    112 

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9.6 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

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184525056 

113 

2.4 

tea 


Tables  of  Reductions  and  Squares 

I  II  III  IT 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

141 

6| 

13585 

184552225 

113 

2.5 

141 

61 

13586 

184579396 

113 

2.6 

141 

61  ' 

13587 

184606569 

113 

2.7 

141 

6J 

13588 

184633744 

113 

2.8 

141 

61 

13589 

184660921 

113 

2.9 

141 

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13590 

184688100 

113 

3.0 

141 

6|. 

13591 

184715281 

113 

3.1 

141 

7 

13592 

184742464 

113 

3.2 

141 

7j 

13593 

184769649 

113 

3.3 

141 

•   71 

13594 

184796836 

113 

3.4 

141 

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13595 

184824025 

113 

3.5 

141 

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13596 

184851216 

113 

3.6 

141 

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13597 

184878409 

113 

3.7 

141 

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13598 

184905604 

113 

3.8 

141 

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13599 

184932801 

113 

3.9 

141 

8 

13600 

184960000 

113 

4.0 

141 

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13601 

184987201 

113 

4.1 

141 

81 

13602 

185014404 

113 

4.2 

141 

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13603 

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113 

4.3 

141 

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13604 

185068816 

113 

4.4 

141 

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13605 

185096025 

113 

4.5 

141 

81 

13606  ; 

185123236 

113 

4.6 

141 

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13607 

185150449 

113 

4.7 

141 

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13608 

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113 

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141 

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13609  ' 

185204881 

113 

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141 

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13610 

185232100 

113 

5.0 

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13611 

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113 

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13612 

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113 

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13614 

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113 

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141 

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13615 

185368225 

113 

5.5 

141 

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13616 

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113 

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141 

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13617 

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113 

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141 

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13618 

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113 

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13619 

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113 

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13620 

185504400 

113 

6.0 

141 

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13621 

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113 

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141 

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13622 

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113 

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141 

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13623 

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113 

6.3 

141 

11 

13624 

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113 

6.4 

141 

iH 

13625 

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113 

6.5 

141 

Hi 

13626 

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113 

6.6 

141 

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13627  , 

185695129 

113 

6.7 

141 

ii£ 

13628 

185722384 

113 

6.8 

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13629  j 

185749641 

113 

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13630 

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113 

7.0 

141 

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13631 

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113 

7.1 

142 

0 

13632  ! 

185831424 

113 

7.2 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet.  Inches 
and  Tenths 

Feet 

Inches 

Feet 

bMfcei 

142 

OJ 

13633    185858689 

113 

7.3 

142 

Oj. 

13634    185885956 

113 

7.4 

142 

01 

13635  ;  185913225 

113 

7.5 

142 

Oi 

13636  !  185940496 

113 

7.6 

142 

Of 

13637    185967769    113 

7.7 

142 

01 

13638    185995044    113 

7.8 

142 

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13639  i  186022321    113 

7.9 

142 

1 

13640    186049600    113 

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142 

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13641 

186076881 

113 

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142 

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13642    186104164 

113 

8.2 

142 

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13643    186131449 

113 

8.3 

142 

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13644 

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113 

8.4 

142 

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13645 

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113 

8.5 

142 

11 

13646 

186213316 

113 

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142 

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13647 

186240609 

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8.7 

142 

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13648 

186267904 

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142 

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13649 

186295201 

113 

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142 

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13650 

186322500 

113 

9.0 

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2f 

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186349801 

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13652 

186377104    113 

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13653 

186404409    113 

9.3 

142 

21 

13654 

186431716    113 

9.4 

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186459025  j  113 

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142 

3 

13656    186486336    113 

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142 

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13657  i  186513649    113 

9.7 

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3* 

13658    186540964 

113 

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142 

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13660 

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113 

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142 

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113 

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142 

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13664 

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113 

10.4 

142 

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13665 

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113 

10.5 

142 

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186759556  |  113 

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142 

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13667 

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113 

10.7 

142 

4J 

13668 

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10.8 

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13669 

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13670 

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13672    186923584 

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187060329 
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113 
113 

11.7 
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142 

13679 

187115041 

113 

11.9 

142 

6 

13680    187142400 

114 

0.0 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

142 

6J 

13681 

187169761 

114 

0.1 

142 

6J 

13682 

187197124 

114 

0.2 

142 

6! 

13683 

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114 

0.3 

142 

6* 

13684 

187251856 

114 

0.4 

142 

61 

13685 

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114 

0.5 

142 

61 

13686 

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114 

0.6 

142 

6£ 

13687 

187333969 

114 

0.7 

142 

7 

13688 

187361344 

114 

0.8 

142 

7k 

13689 

187388721 

114 

0.9 

142 

n 

13690 

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114 

1.0 

142 

n 

13691 

187443481 

114 

1.1 

142 

n 

13692 

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114 

1.2 

142 

7| 

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114 

1.3 

142 

7| 

13694 

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114 

1.4 

142 

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13695 

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114 

1.5 

142 

8 

13696 

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114 

1.6 

142 

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114 

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114 

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114 

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114 

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114 

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114 

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114 

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142 

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114 

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114 

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142 

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114 

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114 

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142 

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114 

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114 

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13710 

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114 

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13711 

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114 

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13712 

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114 

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13714 

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114 

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13717 

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13718 

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114 

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13720 

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114 

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142 

m 

13721 

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114 

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13722 

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114 

4.2 

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111 

13723 

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114 

4.3 

142 

11J 

13724 

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114 

4.4 

142 

lit 

13725 

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142 

11|    13726    188403076  !  114* 

4.6 

142 

m 

13727    188430529    114 

4.7 

143 

0 

13728    188457984    114 

4.8 

Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

cnTTARVQ     Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

143 

01 

13729  .   188485441    114 

4.9 

143 

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13730    188512900    114 

5.0 

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13731  !  188540361    114 

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01 

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13733    188595289    114 

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143 

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5.4 

143 

01    13735    188650225    114 

5.6 

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1   ;  13736  ,  188677696  :  114 

5.6 

143 

14    13737  !  188705169    114 

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143 

lj    13738    188732644 

114 

5.8 

143 

If    13739    188760121 

114 

5.9 

143 

1J 

13740    188787600 

114 

6.0 

143 

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13741    188815081 

114 

6.1 

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1|    13742    188842564 

114 

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li    13743  !  188870049    114 

6.3 

143 

2     13744  i  188897536    114 

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6.5 

143 

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13747 

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13748    189007504 

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13749    189035001 

114 

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143 

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13750    189062500 

114 

7.0 

143 

21 

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3 

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114 

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114 

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114 

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114 

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M 


Tables  of  Reductions  and  Squares 


Eighths 
Feet,  Inches     and 
and  Eighths    Tenths 
i  of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches  i 

Feet 

Inches 

143 

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114 

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114 

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114 

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114 

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114 

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115 

2.4 

Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES   !   2&SST 

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— 

Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

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Tables  of  Reductions  and  Squares 

I  II  III  IV 


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Tables  of  Reductions  and  Squares 

I  II  III  IT 


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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.Inches 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
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Tenths 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet.Inches 
and  Eighths 

Eighths 
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Tenths 
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Tables  of  Reductions  and  Squares 

I  II  III  IV 


Eighths 
Feet,  Inches     and 
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Tables  of  Reductions  and  Squares 


Eighths 
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202066225 

118 

5.5 

148 

1 

14216 

202094656 

118 

5.6 

148 

U 

14217 

202123089 

118 

5.7 

148 

Ii 

14218 

202151524 

118 

5.8 

148 

U 

14219 

202179961 

118 

5.9 

148 

1J 

14220 

202208400 

118 

6.0 

148 

if 

14221 

202236841 

118 

6.1 

148 

if 

14222 

202265284 

118 

6.2 

148 

N 

14223 

202293729 

118 

6.3 

148 

2 

14224 

202322176 

118 

6.4 

148 

2J 

14225 

202350625 

118 

6.5 

148 

2* 

14226 

202379076 

118 

6.6 

148 

2| 

14227 

202407529 

118 

,   6.7 

148 

2J 

14228 

202435984 

118 

6.8 

148 

2| 

14229 

202464441 

118 

6.9 

148 

21 

14230 

202492900 

118 

7.0 

148 

21 

14231 

202521361 

118 

7.1 

148 

3 

14232 

202549824 

118 

7.2 

148 

3J 

14233 

202578289 

118 

7.3 

148 

3* 

14234 

202606756 

118 

7.4 

148 

3| 

14235 

202635225 

118 

7.5 

148  ' 

3* 

14236 

202663696 

118 

7.6 

148 

3f 

14237 

202692169 

118 

7.7 

148 

3} 

14238 

202720644 

118 

7.8 

148 

3& 

14239 

202749121 

118 

7.9 

148 

4 

14240 

202777600 

118 

8.0 

148 

4j 

14241 

202806081 

118 

8.1 

148 

4J 

14242 

202834564 

118 

8.2 

148 

4| 

14243 

202863049 

118 

8.3 

148 

4J 

14244 

202891536 

118 

8.4 

148 

4f 

14245 

202920025 

118 

8.5 

148 

14246 

202948516 

118 

8.6 

148 

4J 

14247 

202977009 

118 

8.7 

148 

5 

14248 

203005504 

118 

8.8 

148 

51 

14249 

203034001 

118 

8.9 

148 

5* 

14250 

203062500 

118 

9.0 

148 

H 

14251 

203091001 

118 

9.1 

118 

5* 

14252 

203119-504 

118 

9-2 

148 

51 

14253 

203148009 

118 

9.3 

148 

14254 

•2(  131  76516 

118 

9.4 

148 

5j 

14255 

2032050-"' 

118 

9.5 

148 

6 

14-_>:>»i 

203233536    1  1  - 

9.6 

m 


Tables  of  Reductions  and  Squares 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet 
and 

,  Inches 
Tenths 

Feet 

Inches 

Feet 

Inches 

148 

6* 

14257 

203262049 

118 

9.7 

148 

6J 

14258 

203290564 

118 

9.8 

148 

61 

14259 

203319081 

118 

9.9 

148 

6J 

14260 

203347600 

118 

10.0 

148 

6f 

14261 

203376121 

118 

10.1 

148 

6| 

14262 

203404644 

118 

10.2 

148 

« 

14263 

203433169 

118 

10.3 

148 

7 

14264 

203461696 

118 

10.4 

148 

7* 

14265 

203490225 

118 

10.5 

148 

7J 

14266 

203518756 

118 

10.6 

148 

7| 

14267 

203547289 

118 

10.7 

148 

1h 

14268 

203575824 

118 

10.8 

148 

7| 

14269 

203604361 

118 

10.9 

148 

7| 

14270 

203632900 

118 

11.0 

148 

7| 

14271 

203661441 

118 

11.1 

148 

8 

14272 

203689984 

118 

11.2 

148 

8J 

14273 

203718529 

118 

11.3 

148 

8J 

14274 

203747076 

118 

11.4 

148 

8| 

14275 

203775625 

118 

11.5 

148 

8J 

14276 

203804176 

118 

11.6 

148 

8| 

14277 

203832729 

118 

11.7 

148 

8} 

14278 

203861284 

118 

11.8 

148 

8i 

14279 

203889841 

118 

11.9 

148 

9 

14280 

203918400 

119 

0.0 

148 

9£ 

14281 

203946961 

119 

0.1 

148 

94 

14282 

203975524 

119 

0.2 

148 

9| 

14283 

204004089 

119 

0.3 

148 

9J 

14284 

204032656 

119 

0.4 

148 

91 

14285 

204061225 

119 

0.5 

148 

9i 

14286 

204089796 

119 

0.6 

148 

9| 

14287 

204118369 

119 

0.7 

148 

10 

14288 

204146944 

119 

0.8 

148 

IOJ 

14289 

204175521 

119 

0.9 

148 

10* 

14290 

204204100 

119 

1.0 

148 

lot 

14291    204232681 

119 

1.1 

148 

10J 

14292 

204261264 

119 

1.2 

148 

10| 

14293 

204289849 

119 

1.3 

148 

10| 

14294 

204318436 

119 

1.4 

148 

10| 

14295 

204347025 

119 

1.5 

148 

11 

14296 

204375616 

119 

1.6 

148 

"i 

14297 

204404209 

119 

1.7 

148 

ill 

14298 

204432804 

119 

1.8 

148 

iif 

14299 

204461401 

119 

1.9 

148 

ii| 

14300 

204490000 

119 

2.0 

148 

in 

14301 

204518601 

119 

2.1 

148 

ni 

14302 

204547204 

119 

2.2 

148 

n* 

14303 

204575809 

119 

2.3 

149 

o 

14304    204604416 

119 

2.4 

Tables  of  Reductions  and  Squares 


IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet   Inches 

149 

OJ    14305    204633025 

119 

2.5 

149 

0}    14306    204661636 

119 

2.6 

149 

Of 

14307 

204690249 

119 

2.7 

149 

o* 

14308 

204718864 

119 

2.8 

149 

01 

14309 

204747481 

119 

2.9 

149 

Of 

14310 

204776100 

119 

3.0 

149 

01 

14311 

204804721 

119 

3.1 

149 

1 

14312 

204833344 

119 

3.2 

149 

li 

14313  !  204861969 

119 

3.3 

149 

1J    14314  :  204890596 

119 

3.4 

149 

If    14315  1  204919225 

119 

3.5 

149 

1£    14316  !  204947856 

119 

3.6 

149 

If    14317    204976489 

119 

3.7 

149 

It 

14318 

205005124 

119 

3.8 

149 

|j 

14319 

205033761 

119 

3.9 

149 

2 

14320 

205062400 

119 

4.0 

149 

2J 

14321 

205091041 

119 

4.1 

149 

2J 

14322 

205119684 

119 

4.2 

149 

2| 

14323 

205148329 

119 

4.3 

149 

14324    205176976 

119 

4.4 

149 

H 

14325  j  205205625 

119 

4.5 

149 

2| 

14326    205234276 

119 

4.6 

149 

21 

14327 

205262929 

119 

4.7 

149 

3 

14328 

205291584 

119 

4.8 

149 

3J 

14329    205320241 

119 

49' 

149 

3J 

14330    205348900 

119 

5.0 

149 

3| 

14331 

205377561 

119 

5.1 

149 

3* 

14332 

205406224 

119 

5.2 

149 

3| 

14333    205434889 

119 

5.3 

149 

3| 

14334    205463556 

119 

5.4 

149 

14335    205492225 

119 

5.5 

149 

4*    14336    205520896 

119 

6.6 

149 

4J  1  14337 

205549569 

119 

5.7 

149 

4i 

14338    205578244 

5.8 

149 

4§ 

14339 

205606921 

119 

5.9 

149 

14340 

205635600 

119 

6.0 

149 

4| 

14341 

205664281 

119 

6.1 

149 

14342 

205692964 

119 

6.2 

149 

4& 

14343 

205721649 

119 

6.3 

149 

5 

14344 

205750336 

119 

6.4 

149 

14345 

205779025 

119 

6.5 

149 

5* 

14346 

205807716 

119 

6.6 

149 

H 

14347 

205836409 

119 

6.7 

149 

14348 

205865104 

119 

6.8 

149 

5| 

14349 

205893801 

119 

6.9 

149 

14350 

205922500 

119 

7.0 

149 

5} 

14351 

205951201 

119 

7.1 

149 

6 

14352    205979904    119 

7.2 

Tables  of  Reductions  and  Squares 

I  II  III  IV 


Feet,  Inches 
and  Eighths 

Eighths 
and 
Tenths 
of  Inches 

SQUARES 

Feet,  Inches 
and  Tenths 

Feet 

Inches 

Feet 

Inches 

149 

6& 

14353 

206008609 

119 

7.3 

149 

6J 

14354 

206037316 

119 

7.4 

149 

6| 

14355 

206066025 

119 

7.5 

149 

6* 

14356 

206094736 

119 

7.6 

149 

6| 

14357 

206123449 

119 

7.7 

149 

6| 

14358 

206152164 

119 

7.8 

149 

6f 

14359 

206180881 

119 

7.9 

149 

7 

14360 

206209600 

119 

8.0 

149 

7J. 

14361 

206238321  !  119 

8.1 

149 

u 

14362 

206267044    119 

8.2 

149 

7| 

14363 

206295769    119 

8.3 

149 

n 

14364 

206324496    119 

8.4 

149 

7| 

14365 

206353225    119 

8.5 

149 

74 

14366 

206381956    ll'.» 

8.6 

149 

u 

14367 

206410689    119 

8.7 

149 
149 

8 

14368 
14369 

206439424 
206468161 

119 
119 

8.8 
8.9 

149 

H 

14370 

206496900 

119 

9.0 

149 

8| 

14371 

206525641 

119 

9.1 

149 

8* 

14372 

206554384 

119 

9.2 

149 

8| 

14373 

206583129 

119 

9.3 

149 

8f 

14374 

206611876 

119 

9.4 

149 

14375 

206640625 

119 

9.5 

149 

9 

14376 

206669376 

119 

9.6 

149 

9j 

14377 

206698129 

119 

9.7 

149 

9J 

14378 

206726884 

119 

9.8 

149 

9| 

14379 

206755641 

119 

9.9 

149 

9* 

14380 

206784400 

119 

10.0 

149 

9| 

14381 

206813161 

119 

10.1 

149 

9f 

14382 

206841924 

119 

10.2 

149 

H 

14383 

206870689 

119 

10.3 

149 

10 

14384 

206899456 

119 

10.4 

149 

10J 

14385 

206928225 

119 

10.5 

149 

IQ\ 

14386 

206956996 

119 

10.6 

149 

10| 

14387 

206985769 

119 

10.7 

149 

10* 

14388 

207014544 

119 

10.8 

149 

10| 

14389 

207043321 

119 

10.9 

149 

10| 

14390 

207072100 

119 

11.0 

149 

101 

14391 

207100881    119 

11.1 

149 

11 

14392 

207129664    119 

11.2 

149 

111 

14393 

207158449    119 

11.3 

149 

111 

14394 

207187236 

119 

11.4 

149 

llf 

14395 

207216025 

119 

11.5 

149 

11* 

14396 

207244816 

119 

11.6 

149 

llf 

14397 

207273609 

119 

11.7 

149 

111 

14398 

207302404    119 

11.8 

149 

111 

14399 

207331201    119* 

11.9 

150 

0     14400 

207360000    120 

0.0 

Table  of  Pitches  per  Foot. 

The  first  column  contains  the  amount  of  rise 
per  foot,  beginning  with  1  inch  and  running  by 
sixteenths  to  18  inches.  The  ratio  column  gives 
the  ratio  of  vertical  rise  to  horizontal  run  in 
whole  numbers  (eliminating  the  fraction).  The 
two  columns  at  the  right  give  hypothenuse-lengths 
in  eighth  inches,  the  first  column  giving  the 
length  of  the  hypothenuse  or  oblique  line  when 
the  horizontal  distance  or  base  is  an  eighth  of  an 
inch,  the  second  column  giving  the  length  of 
hypothenuse  for  a  base  of  1  foot. 

For  example,  an  oblique  line  rises  7-jV  *n  a 
horizontal  distance  of  1  foot.  The  ratio  of  rise 
to  run  is  115  to  192  (see  Ratio  Column).  The 
next  column  gives  the  length  of  this  oblique  line 
where  it  has  passed  over  a  horizontal  distance  of 
an  eighth  of  an  inch,  in  this  case  1.1656  (eighths). 
If  there  is  a  rafter  whose  pitch  is  7TV  per  foot 
and  whose  base  is  25'  0",  the  rafter  length  is 
found  thus :  25'  0"  =  2400  (eighths,  table  of 
Reductions).  1.1656  X  2400  =  2797.44  =  (by 
table  of  Reductions)  29'  1  j|"  =  rafter  length 
(.44  approximates  half  of  an  eighth).  When 
the  base  is  given  in  even  feet,  however,  as  in 
this  case,  it  will  be  more  convenient  to  use  the 
last  column,  in  which  the  length  of  the  hypoth- 
enuse is  given  in  eighths  for  a  base  of  1  foot. 
Then  the  rafter  length  =  111.90  (last  column) 
X  25  =  2797.50  ==  29'  1JJ". 

The  following  problem  contains  several  illus- 
trations of  the  use  of  this  table  : 


'above  cf- 


(a)  (6)  (//.)  is  one  side  -of  a  gable  roof  whose 
rise  per  foot  is  12^-"  and  which  is  intersected 
by  a  lower  roof  whose  plate  is  3'  6"  lower  than 
that  of  the  first  roof  and  whose  rise  per  foot  is 
10£".  16'  2i"  =1556  eighths.  Find  12^-" 
in  first  colum  of  table  of  Pitches  per  foot ;  then 
the  ratio  of  the  roof  is  197  (rise)  to  192  (run) 
and  the  height  equals  !-^g^  =  1596.52  =  16' 
7|"  (see  Ratio,  page  11,  vol.  I).  12'  6|"  = 
1204.  The  ratio  of  inclination  for  roof  (c)  (d)  is 
82  to  96  =  41  to  48,  and  the  height  of  that  roof 
equals  12M48X4t  =  1028.4  =  10'  8£".  10'  8|"  - 
3'  6"  =  7'  2|"=  height  of  lower  ridge  above 
the  upper  plate,  (v)  (w]  = '.'  ~'k'^ 102  =  — ,^=  = 
674 4  =  1'  Oi".  (C)(«)  =  »l<^  =  »£«•  = 
393.3  =  4'  li".  (e)  (w)  =  12'  6J"  —  4'  1|" 
=  8'  5f".  The  ratio  (v)  (w)  to  (w)  (e)  equals 
(<?)  (/)  to  (w)  (w}  =  V  Oi"  to  8'  5f  "  =  674.4  to 
810.7,  hence  (c)  (/)  =  m8X7674-4  =  327  =  3'  4£". 
The  point  (/)  is  located  under  the  supposition 
that  the  valley  is  to  be  extended  through  to  the 
lower  plate.  16'  2|"  =  1556  eighths  and  the 
rafter  length  (a)  (6)  =  1556  X  1.4327  (table  of 
Pitches  per  foot)  =  2229.28  =  23'  2f ".  Rafter 
length  (c\  (w)  =  1204  X  1.3151  =  1583.48  = 
16'  5£". 

In  order  to  find  the  pitch  per  foot  of  a  roof 
whose  inclination  is  known.  If  the  ratio  for 
example  were  263  rise  to  197  run,  12"  =  96 
eighths  9-^-3  =  128  to  96 

263 
96 

1578 
2367 


197)25248(128 
197 

~554 
394 

1608 
1576 


This  ratio  may  be  found  in  the  Ratio  Column 
of  the  table  of  Pitches  per  foot  and  adjoining  is 
given  the  pitch  per  foot,  16  inches,  or  128  may 
be  looked  for  in  the  column  of  eighths,  Table  of 
Reductions.  128  eighths  =  1'  4"  =  16  inches. 

In  the  case  of  a  hip  at 
the  intersection  of  roofs 
of  the  same  pitch  this 
table  will  give  the  lengths 
of  cripple  rafters.  The 
plan  of  rafter  (1}  equals 
(la).  Then  if  the  pitch 
is  9i"  per  foot  and  if 
(la)=l  foot,  the  crip- 
ple length  equals  122.44  eighths  =  1'  3J". 
2  a  =  cripple  3  feet  away  =  3  X  122.44  = 
367.32  =  3'  9i". 


a 


Table  of  Pitches  per  Foot 


Rise 
per  Foot 

In  Inches 

Ratio 

Hypothenuse  on 
Base  of 
an  Eighth  Inch 

In  Eighths 

Hypothenuse 
on  Base  of 
One  Foot 

In  Eighths 

Rise 

Run 

1 

8 

96 

1.0035 

96.34 

1A 

17 

192 

1.0040 

96.38 

H 

9 

96 

1.0044 

96.42 

1&           19 

192 

1.0049 

96.47 

H          10 

96 

1.0054 

96.52 

1A 

20 

192 

1.0060 

96.58 

if 

11 

96 

1.0065 

96.63 

23 

192 

1.0072 

9669 

If 

12 

96 

1.0077 

96.74 

1A 

25 

192 

1.0084 

96.81 

if 

13 

96 

1.0091 

96.87 

27 

192 

1.0098 

96.94 

if 

14 

96 

1.0106 

97.02 

ill 

29 

192 

1.0113 

97.09 

if 

15 

96 

1.0122 

97.17 

i« 

31 

192 

1.0129 

97.24 

2 

16 

96 

1.0138 

97.32 

2A 

33 

192 

1.0146 

97.40 

2£ 

17 

96 

1.0156 

97.50 

2A 

35 

192 

1.0164 

97.58 

18 

96 

1.0175 

97.68 

2T5S 

37 

192 

1.0184 

97.77 

,    2t 

19 

96 

1.0194 

97.86 

2yV 

39 

192 

1.0204 

97.96 

2* 

20 

96 

1.0215 

98.06 

2A 

41 

192 

1.0225 

98.16 

2| 

21 

96 

1.0236 

98.27 

2H 

43 

192 

1.0248 

98.38 

2| 

22 

96 

1.0259 

98.49 

gj| 

45 

192 

1.0271 

98.60 

2& 

23 

96 

1.0283 

98.72 

2i| 

47 

192 

1.0296                   98.84 

3 

24 

96 

1.0308                   98.96 

SA 

49 

192 

1  .0321 

99.08 

34 

25 

96 

1.0333 

99.20 

SA 

51 

192 

1.0347 

99.33 

3} 

%    26 

96 

1.0361 

99.46 

3A 

53 

192 

1  0374 

99.59 

3| 

27 

96 

1.0389 

99.73 

3A 

55 

192 

1.0402 

99.86 

28 

.   96 

1.0417          ;        100.00 

3A 

57 

192 

1.0431 

100.14 

3| 

29 

96 

1.0447 

100.29 

3H 

59 

192 

1.0461 

100.43 

3| 

30 

96 

1.0477 

100.58 

3H 

61 

192 

1.0492 

100.73 

3* 

31 

96 

1.0508 

100.88 

3M 

G3 

192 

1  0525 

101  .04 

Table  of  Pitches  per  Foot 


Rise                Ratio 
per  Foot 

Uypothenu.se  on 
Base  of 
an  Eighth  Inch 

In  Eighths 

Hypothenuse 
on  Base  of 
One  Foot 

In  Eighths 

In  Inche^ 

Run 

4               32         96 

1.0540 

101.19 

4^           65        192 

1.0557 

101.35 

4J            33 

96 

1.0574 

101.51 

4A           67 

192 

1.0591 

101.68 

4*             34 

96 

1.0608 

101.84 

4A    i      69 

192 

1.0626 

102.01 

4|             35 

96 

1.0644 

102.18 

4  A     :      71 

192 

1.0661 

102.35 

4£             36 

96 

1.0680 

102.53 

4&     i      73 

192 

1.0699 

102.71 

4|             37 

96 

1.0716 

102.88 

4H           75 

192 

1.0735 

103.06 

4}             38 

96 

1.0755 

103.25 

4H           77 

192 

1.0774 

103.43 

4£            39 

96 

1.0794 

103.62 

4B           79  i     192 

1.0813 

103.81 

5              40         96 

1.0833 

10400 

5TV           81 

192 

1.0853 

104.19 

5J-            41 

% 

1.0874 

104.39 

5T3y           83 

192 

1.0894 

104.59 

5J             42 

96 

1.0915 

104.78 

5&           85 

192 

1.0935 

104.98 

5|            43 

96 

1.0957 

105.19 

5TV           87 

192 

1.0979 

105.40 

£          44 

96 

1.1000 

105.60 

&A   1    89 

192 

1.1022 

105.81 

5|            45  |      96 

1.1044 

106.02 

6ft-  1      91       192 

1.1066 

106.24 

5|            46  j      96 

1.1088 

106.45 

5H           93       192 

1.1111 

106.67 

5£            47 

96 

1.1134 

KM  n 

511           95 

192 

1.1157 

107.11 

6              48 

96 

1.1180 

1  07.  3:t 

6^           97 

192 

1.1204 

107.66 

6&            49 

.... 

1.1228 

107.78 

6^           99 

192 

1.1251 

108.01 

6t            50 

96 

1.1275 

108.24 

6A         101 

192 

1.1299 

108.47 

6|            51 

96 

1.1323 

108.70 

6fV         ]03 

192 

1.1348 

108.94 

6i             52 

96 

1.1373 

109.18 

6A         105 

192 

1.1397 

L09.4J 

VI6 

6|            53 

M 

1.1423 

|(M  M 

6H         107 
6J            54 

192 
96 

1.1448 

1.1171 

L10.16 

V4 

6}t         109 
6J            55 

192 
96 

1.1499 
1.1525 

L10.M 

110.64 

1.1551 

110.89 

309 


Table  of  Pitches  per  Foot 


per  Foot   | 

In  Inches  j    Rise    j   Run 


Hypothenuse  on 

Base  of 
an  Eighth  Inch 

In  Eighths 


Hypothenuse 
on  Base  of 
One  Foot 

In  Eighths 


7 

56 

96 

1.1577 

111.14 

7rV 

113 

192 

1.1603 

111.39 

7| 

57 

96 

1.1630 

111.65 

7A 

115 

192 

1.1656 

111.90 

n 

58 

96 

1.1683 

112.16 

7A 

117 

192 

1.1710 

112-42 

7| 

59 

96 

1.1737 

112.68 

7A 

119 

192 

1.1764 

112.94 

7* 

60 

96 

1.1792 

113.21 

7r9^ 

121 

192 

1.1820 

113.47 

7| 

61 

96 

1.1848 

113.74 

7yi 

123 

192 

1.1876       114.01 

7| 

62 

96 

1.1904       114.28 

7H 

125 

192 

1.1932       114.55 

71 

63 

96 

1.1960       114.82 

7yf 

127 

192 

1.1989       115.10 

8 

64 

96     1.2018 

115.38 

8iV 

129 

192 

1.2047 

115.65 

8J 

65 

96 

1.2077 

115.94 

8A 

131 

192 

1.2105 

116.21 

8i 

66 

96 

1.2135 

116.50 

8A 

133 

192 

1.2165 

116.78 

8| 

67 

96 

1.2194       117.07 

135 

192 

1.2225       117.36 

8* 

68 

96 

1.2255       117.65 

8  9 

137 

192 

1.2284       117.93 

8| 

69 

96 

1.2316       118.23 

8H 

139 

192 

1.2345 

118.51 

8i 

70 

96 

1.2376 

118.81 

SB 

141 

192 

1.2407 

119.11 

8|- 

71 

96 

1.2438 

119.41 

8ri 

143 

192 

1.2468 

119.70 

9 

72 

96 

1.2500 

120.00 

9iV 

145 

192 

1.2531 

120.30 

9J     73 

96 

1.2562 

120.60 

9A    147 

192 

1.2595 

120.91 

9J     74 

96 

1.2626 

121.21 

9T»5 

149 

192 

1.2658 

121.52 

9|     75 

96 

1.2690 

121.83 

9A    151 

192 

1.2722 

122.13 

9*     76 

96 

1.2754 

122.44 

9A    153 

192 

1.2786 

122.75 

9|     77 

96 

1.2818 

123.06 

9H    I55 

192 

1.2852 

123.38 

9|     78 

96 

1.2884 

123.70 

9H  '  I57 

192     1.2917       124.01 

9£     79 

96 

1.2951       124.33 

9H    159 

192 

1.2983       124.64 

Table  of  Pitches  per  Foot 


Rise 
per  Foot 

Ratio 

Hypothenuse  on 

B..M-    ,.f 

an  Eighth  Inch 
In  Eighths 

Hypothenuse 
on  Base  of 
One  Foot 

In  Eighths 

In  Inches 

Rise 

Run 

10 

80         96 

1.3017 

124.96 

10^ 

161 

192 

1.3050 

125.28 

10J 

81 

96 

1.3084 

125.61 

IOA 

163 

192 

1.3118 

125.93 

lot 

82         96 

1.3151 

126.25 

IOA 

165 

192 

1.3185 

126.58 

10|             83 

96 

1.3220 

126.91 

IOA         167 

192 

1.3253 

127.23 

10*             84 

96 

1.3288                 127.56 

10&         169 

192 

1.3322 

127.89 

10t 

85 

96 

•  1.3356 

128.22 

IOH 

171 

192 

1.3391 

128.55 

10} 

86 

96 

1.3426 

128.89 

173 

192 

1.3460 

129.22 

lot 

87 

96 

1.3494 

129.55 

175 

192 

1.3530 

129.89 

11  * 

88 

96 

1.3566 

130.23 

HA 

177 

192 

1.3601 

130.57 

lit 

89 

96 

1.3636 

130.91 

HA 

179 

192 

1.3672 

131.25 

lit 

90 

96 

1.3707 

131.59 

181 

192 

1.3743 

131  .93 

HI 

91 

96 

1.3778 

132.27 

HA 

183 

192 

1.3815 

132.62 

Hi 

92 

96 

1.3850                 132.96 

HA 

185 

192 

1.3886 

133.31 

93 

96 

1.3923 

133.66 

iiH 

187 

192 

1.3959 

134  Jttl 

11; 

94 

96 

1.3995 

134.36 

189 

192 

1.4032                 134.71 

Hi 

95 

96  i         1-4069                 135.06 

1HI 

191 

192            1.4105                 135.41 

12 

96 

96 

1.4142 

135.76 

193 

192 

1.4179 

136.12 

97 

96 

1.4216 

136.47 

195 

192 

1.4253 

136.83 

12} 

98 

M 

1.4291                 137.19 

«A 

197 

192 

1.4327 

12| 

99 

96 

1.4365                 137.90 

1  w       192            1.4402 

12™ 

100         96 

1.4439- 

12& 

201 
101 

192 
96 

1  .4477 
1.4515 

1>  H 
139.34 

12H 
12} 

203 
102 

192 
96 

1.4552 
1.4591 

139.70 
140.07 

i-_>!.: 

m 

192            LOT 

103 

gr,           L.4M8 

12H 

207 

199            1.4705                M1.17 

.11 


Table  of  Pitches  per  Foot 


Rise   • 
per  Foot 

Ratio 

Hypothenuse  on 
Base  of 
an  Eighth  Inch 

In  Eighths 

Hypothenuse 
on  Base  of 
One  Foot 

In  Eighths 

In  Inches 

Rise 

Run 

13 

104 

96 

1.4743 

141.53 

ISA 

209 

192 

.4781 

141.90 

13| 

105 

96 

.4820 

142.27 

ISA 

211 

192 

1.4858 

142.64 

13J 

106 

96 

.4897 

143.01 

1»A 

213 

192 

.4935 

143.38 

13| 

107 

96 

.4975 

143.76 

ISA 

215 

192 

.5013 

144.13 

m 

108 

96 

1.5052 

144.50 

ISA 

217 

192 

1.5091 

144.87 

13| 

109 

96 

1.5130 

145.25 

IStt 

219 

192 

1.5169 

145.62 

13| 

110 

96 

1.5208 

146.00 

13H 

221 

192 

1.5248 

146.38 

1«J 

111 

96 

1.5287 

146.75 

13JI 

223 

192 

1.5323 

147.13 

14 

112 

96 

1.5366 

147.51 

WA 

225 

192 

1.5406 

147.90 

14* 

113 

96 

1.5445 

148.27 

14& 

227 

192 

1.5484 

148.65 

Hi 

114 

96 

1.5525 

149.04 

MA 

229 

192 

1.5565 

149.42 

14| 

115 

96 

1.5605 

149.81 

14A 

231 

192 

1.5644 

150.18 

14* 

116 

96 

1.5684 

150.57 

14T9* 

233 

192 

1.5725 

150.96 

14| 

117 

'   96 

1.5765 

151.34 

14H 

235 

192 

1.5805 

151.73 

14| 

118 

96 

1.5646 

152.12 

14H 

237 

192 

1.5886 

152.51 

14J 

119 

96 

1.5927 

152.90 

14H 

239 

192 

1.5967 

153.28 

15 

120 

96 

1.6008 

153.68 

15A 

241 

192 

1.6048 

154.06 

m 

121 

96 

1.6089 

154.46 

l&A 

243 

192 

1.6130 

154.85 

15J 

122 

96 

1.6171 

155.24 

ISA 

245 

192 

1.6211 

155.63 

15f 

123 

96 

1.6253 

156.03 

16A 

247 

192 

1.6294 

156.42 

15* 

124 

96 

1.6335 

156.82 

l&T9* 

249 

192 

1.6376 

157.21 

16| 

125 

96 

1.6418 

157.61 

15H 

251 

192 

1.6459 

158.01 

15| 

126 

96 

1.6500 

158.40 

15B 

253 

192 

1.6542 

158.80 

16| 

127 

96 

1.6583 

159.20 

15*1 

255 

192 

1.6625 

159.60 

Table  of  Pitches  per  Foot 


Rise 
per  Foot 

Ra 

tio 

Hypothenuse  on 
Base  of 

Hypothenuse 
on  Base  of 

In  Inches 

Rise 

Run 

In  Eighths 

In  Eighths 

16 

128 

96' 

1.6666 

160.00 

IfjyV 

257 

192 

1.6708 

160.40 

16J 

129 

96 

1.6750 

160.80 

16A 

259 

192 

1.6792 

161.20 

16^ 

130 

96 

1.6833 

161.60 

1&& 

261 

192 

1.6876 

162.01 

161° 

131 

96 

1.6918 

162.41 

263 

192 

.6959 

162.81 

16** 

132 

96 

.7002 

163.22 

265 

192 

.7044 

163.62 

16f* 

133 

96 

.7086 

164.03 

267 

192 

.7128 

164.43 

16| 

134 

96 

.7171 

164.84 

JglS 

269 

192 

.7213 

165.25 

167 

135 

96 

.7255 

165.65 

16^ 

271 

192 

.7298 

166.06 

17 

136 

96 

.7341 

166.47 

273 

192 

.7383 

166.88 

,-T* 

137 

96 

.7426 

167.29 

17  A 

275 

192 

.7469 

167.70 

,_T 

138 

96 

.7511 

168.11 

17^ 

277' 
139 

192 
96 

.7554 
.7597 

168.52 
168.93 

17 

279 

192 

.7640 

169.34 

17* 

140 
281 

96 
192 

.7682 
1.77*5 

169.75 
170.16 

^'_:  ' 

141 

96 

1.7769 

170.58 

17H 
1711 

174 

17H 

283 
142 
285 
143 
287 
144 

192 
96 
192 
96 
192 
96 

1.7811 
1.7855 
1.7899 
1.7942 
1.7984 
1.8028 

170.99 
171.41 
171.83 
172.24 
172.65 
173.07 

: 


Table  of  Angular  Ratios.* 

This  table  gives  the  ratio  of  vertical  rise  to 
horizontal  run  of  an  inclined  line  for  every  de- 
gree and  minute  between  0°  and  90°.  When- 
ever the  angular  pitch  of  a  roof  is  given  instead 
of  the  base  and  height  the  table  will  prove  invalu- 
able in  determining  the  various  roof  intersec- 
tions, etc.  In  each  coupled  column  the  left  side 
contains  the  altitude  ratio  number  and  the  height 
contains  the  base  ratio  numbers. 

It  will  be  noted  in  passing  over  the  pages  that 
the  headings  pass  from  0°  on  the  first  page  to 
45°  at  the  end  of  the  table;  for  all  angles  over 
45°  pass  back,  finding  the  angle  at  the  bottom  of 
the  page,  reading  up  and  taking  the  right  hand 
column  for  rise  and  left  for  run.  The  following 
problem  illustrates  the  use  of  this  table,  a  roof 
of  half-span  11'  1"  has  a  pitch  of  28°.  What 
is  its  height  ?  The  ratio  of  rise  to  run  is  46947 
to  88295.  For  ordinary  purposes  this  may  be 
taken  as  469  to  883  without  serious  error.  Then 
the  height  equals  UI^«S  =  lil|^  =  590f  = 


*The  table  of  angular  ratios  will  be  recognized  by 
those  familiar  with  trigonometrical  tables  as  a  table  of 
sines  and  cosines. 


014 


Table  of  Angular  Ratio 


BEAD  DOWN 


99982  [  .03633 
99982    .03664! 


99932  .05437 
99931  .05466 
999301  .05495 
99929 1  .05524 
99927  .((Jo:.:! 
99926J  .05582 
99925,  .05611 


00407  .99999 

00436  .99999 

00465  .99999 

00495  .99999 
QQ6M 


00727  -99997 
00756  .99997 
00785  :. 99997 
008141.99997 
00844  .99996 

03902  .99996 
00931 ;. 999%  j 
00960  i. 999951 


010181.99995 

01047  .WWJfi 
01076  .99994 
01105  .99994! 
01134  |.99994 
01164  .WJ93 

onus  .'.we 
012221.99993 
012511.99992 
01280  .99992 
01309  .99991 


.03112 
.03141 
OU70 
.03199 


Table  of  Angular  Ratio 

BEAD  DOWN 
4°  5°  6°  7C 


Mil. 

A 

Kin. 

0 

.06976 

.99756  .08716  .99619  .10453 

.09452  .12187  '.99255 

80 

1 

.07005 

.99754 

.08745  .99617'  .10482 

.90449  .12216  '.99251 

Gfi 

2 

.07034 

.99752  .08774  .99614  .10511 

.99446  .12245,.  99248 

,-g 

3 

.07063 

.99750  !  .08803  ,  .99612  j  .10540 

.09413  .12274  .99244 

.37 

4 

.07092 

.99748  .HNS31;.  99609  i  .10569 

.99440  .12302  .99240 

56 

5 

.07121 

.'.•'.•716  .OSS60  .90607  .10507 

.  99437  i.  12331  .99237 

55 

6 

.07150 

.99744 

.08889 

.99604 

.10626 

.99434!  .12360  .96233 

54 

7 

.07179 

.99742 

.08918  .99602 

.10655 

.99431'  .12389|.99230 

53 

8 

.07208 

.99740 

.08947  .99599 

.10684 

.99428  .12418  .90226 

52 

9 

.07237 

.99738 

.08976 

.99596 

.10713 

.00424  .12447  .00222 

51 

10 

.07266 

.99736 

.09005 

.99594 

.10742 

.99421  ;.  12476  .99219 

50 

11 

.07295 

.99734 

.09034 

.99591 

.10771 

.99418  '.12504  .99215 

49 

12 

.07324 

.99731 

.09063 

.99588 

;.  losoo 

.00115  .12533-99211 

48 

13 

.07353 

.99729 

.09092 

.99586 

.10829 

.  99412  j  .  12562  '.  99208 

47 

14 

.07382 

.90727  .09121 

.99583 

.10858 

.99409'  .12501  .00204  46 

15 

.07411 

.99725 

.09150 

.99580 

.  10887 

.09406  .12620!.  99200  45 

16  i.07440 

.997231  1.09179 

.99578 

.10916 

.90402  .12610  .99197 

44 

17 

.07469 

.99721  .09208 

.99575 

.10945 

.99309  .12678  -.991  93 

43 

18 

.07498 

.99719  .09237 

.99572 

'.10973 

.99396  .  12706  '  99189 

42 

19 

.  07527 

.99716 

.09266 

.90570 

.11002 

.99393  .12735  '.99186 

41 

20 

.07556 

.99714 

.09295 

.99567 

.11031 

.99390  .12764  .99182 

40 

21 

.07585 

.99712 

.09324 

.99564 

.11060 

.99386  .12793  .99178]  39 

22  .07614 

.99710 

.09353 

.98562 

.11089 

.  99383  :  .128221.99175 

ga 

23  .07643 

.99708 

.09382 

.09559 

.11118 

.99380  .12851  .99171 

37 

24  .07672 

.99705 

.09411 

.99556 

.11147 

.99377  .12880  .99167 

36 

25 

.07701 

.99703 

.09440 

.99553 

.11176 

.99374  .12908  .99163 

35 

26 

.07730 

.99701 

.09469 

.99551 

.11205 

.99370  .12937  .09160 

34 

27 

.07759 

.99699 

.09498 

.99548 

.11234 

.99367  .12966  .99156 

33 

28 

.07788 

.99696 

.09527 

.99545 

.11263 

.09364  .12005  .90152 

32 

29 

.07817 

.99694 

.09556 

.99542 

.11291 

.99360  .13024  .99148 

31 

30 

.07846 

.99692 

.C9585  .09540  .11320 

.90357  .13053  .99144 

50 

31 

.07875 

.99689  .09614  .99537  .11349 

.99354  .130S1  .99141 

29 

32 

.07904 

.99687 

.09642  .99534 

.11378 

.99351!  .13110  .99137 

28 

33 

.07933 

.93685 

.09671 

.99531 

.11407 

.9J347  .13139  .99133 

an 

34 

.07962 

.99683 

.09700 

.99528 

.  1  1436 

.99344  -13168  .99129 

26 

35 

.07991 

.99680 

.09729 

.99526 

.  11465 

.9J341  .13197  .99125 

25 

36 

.08020 

.996781  (.09758 

.99523 

.1149-1 

.99337  .13226  '.99122  24 

37 

.08049 

.99676  .09787 

.09520 

.11523 

.99334'  .13254  .99118  23 

38 

.08078 

.99673)  .09816 

.90517  .11552 

.99&31  .13283  .09114  22 

39 

.08107 

.99671  .00845 

.00514  .11580 

.99327!  .13312  .99110  21 

40 

.08136 

.99668  i.  09874 

.00511  .11609 

.99324  .13341  .99106  20 

41 

.08165 

.99666 

.09903 

.  99503  |  .11638 

.99320  '.13370  '.99102  19 

42 

.08194 

.'09664  M.09932 

.99506 

.11667 

.99317  .13399;.  99198  18 

43 

.08223 

.99661  .09961  .99503 

.11696 

.90314  .13427  .99094 

17 

44 

.08252 

.99659!  .09990  .99500 

.11725 

.90310  .13456  .90001 

ie 

45 

.08281 

.99657  .100191.99497 

.11754 

.99307  .13485  .99087 

15 

46 

.08310 

.99654  .10048 

.99494  .11783 

.99303:  13514  .99183 

14 

47 

.08339 

.99652  .10077 

.99491  .11812 

.09300  .13543  .99079 

13 

48 

.08368 

.99649 

.10106 

.99488 

.11840 

.99207  .13572  .09075 

12 

49 

.08397 

.99647  j.  10135 

.99485  .11869 

.99293  .13600^99071 

11 

50  .08426 

.99644  .10164 

.99482  .11898 

.09200  .13629  .99067 

JU 

51  .08455  -90642  .10192 

.00470  .11927  ..99286  .13658  .99063 

B 

52  .08484  .  99639  |j.  10221 

.00476  .11956 

.99283  .13687  .90050 

> 

53  .08513 

.99637  ij.  10250 

.00473  .11085 

.00270  .13716  .99055 

7 

54  .08542 

.  99635  |  .  10279 

.00470  .12014 

.90276  .13744  .99051 

6 

55  .08571  .996321  .10308  .99467  .12043 

.00272  .13773  .99047 

5 

56  .08600 

.00630  .10337  .99464  .12071 

.99266  .138021.99043 

4 

57  1.08629 

.99627 

.10366 

.99461  .12100 

.93265  .13831  .99039 

B 

58  .08658 

.99625 

.10395 

.99458 

.12129 

.09262  .13860  .99035 

2 

59  .08687 

.99622 

.10424 

.99455 

.12158 

.99258,  -13889  '.99031 

1 

60  '.08716 

.99619 

.10453 

.99452 

.12187 

.99255  .13917  .99027 

0 

¥hT 

84°  83° 

BEAD  TJP 

316 


Table  of  Angular  Ratio 


READ  DOWN 
9°  loo 


.96858 

15097 

1 5126  .98845 

15155  .98845 

15184  .98841 

15212 

15241 

15270 


Table  of  Angular  Ratio 

BEAD  DOWN 
12°  13°     -  14°  15° 


Min. 

A 

Min. 

0 

20791 

.97815 

.22495 

97437 

24192 

.97030 

.25882 

96593 

60 

1 

20820 

.97809 

.22523 

97430 

24220 

.97023 

.25910 

96585 

59 

2 

20848 

.97803 

.22552 

97424 

24249 

.97015 

.25938 

96578 

58 

3 

20877 

.97797 

.22580 

97417 

24277 

.97008 

.25966 

96570 

57 

4 

20905 

.97791 

.22608 

97411 

24305 

.97001 

.25994 

96562 

56 

5 

20933 

.97784 

.22637 

97404 

24333 

.96994 

.26022 

96555 

55 

6 

20962 

.97778 

.22665 

97398 

24362 

.96987 

.26050 

96547 

54 

7 

20990 

.97772 

.22693 

97391 

24390 

.96980 

.26079 

.96540 

53 

8 

21019 

.97766 

.22722 

97384 

24418 

.96973 

.26107 

.96532 

52 

9 

21047 

97760 

.22750 

97378 

24446 

.96966 

.26135 

.96524 

51 

JO 

21076 

97754 

.22778 

97371 

24474 

.96959 

.26163 

.96517 

50 

11 

21104 

97748 

22807 

97365 

24503 

.96952 

.26191 

.96509 

49 

12 

21132 

97742 

22835 

97358 

24531 

.96945 

.26219 

.96502 

48 

13 

21161 

97735 

22863 

97351 

24559 

.96937 

.26247 

.96494 

47 

14 

21189 

97729 

22892 

97345 

24587 

.96930 

.26275 

.96486 

46 

15 

21218 

97723 

22920 

97338 

24615 

.96923 

.26303 

.96479 

45 

1C 

21246 

97717 

.22948 

97331 

24644 

.96916 

.26331 

.96471 

44 

17 

21275 

97711 

.22977 

97325 

.24672 

.96909 

.26359 

.96463 

43 

18 

21303 

97705 

.23005 

97318 

.24700 

.96902 

.26387 

.96456 

42 

19 

21331 

97698 

.23033 

97311 

.24728 

.96894 

.26415 

.96448 

41 

20 

21360 

97692 

.23062 

97304 

.24756 

.96887 

.26443 

.96440 

40 

21 

21388 

97686 

.23090 

97298 

.24784 

.96880 

.26471 

.96433 

39 

22 

21417 

97980 

.23118 

97291 

.24813 

.96873 

.26500 

.96425 

38 

23 

21445 

97673 

.23146 

97284 

.24841 

.90866 

.26528 

.96417 

37 

24 

21474 

97667 

.23175 

97278 

.24869 

.96858 

.26556 

.96410 

36 

25 

21502 

97661 

.23203 

97271 

.24897 

.96851 

.26584 

.96402 

35 

26 

21530 

97655 

.23231 

97264 

.24925 

.96844 

.26612 

.96394 

34 

27 

21559 

97648 

.33260 

97257 

.24954 

.96837 

.26640 

.96386 

33 

28 

21587 

97642 

.23288 

97251 

.54982 

.96829 

.26668 

.96379 

32 

29 

21616 

97636 

.23316 

97244 

.25010 

9689f) 

.26696 

.96371 

31 

30 

21644 

97630 

.23345 

97237 

.25038 

.96815 

.26724 

.96363 

:w 

31 

21672 

97623 

.23373 

97230 

.25066 

.96807 

.26752 

.96355 

29 

32 

21701 

97617 

.23401 

97223 

.25094 

.96800 

.26780 

.96347 

28 

3:1 

21729 

97611 

.23429 

97217 

.25122 

.96793 

.26808 

.96340 

27 

34 

21758 

97604 

.23458 

97210 

.25151 

.96786 

.26836 

.96332 

•26 

35 

21786 

97598 

.23486 

97203 

.25179 

.96778 

.26864 

.96324 

25 

3G 

21814 

97592 

.23514 

.97196 

.25207 

.96771 

.26892 

.96316 

24 

37 

21843 

97585 

.23542 

97189 

.25235 

.96764 

.26920 

.96308 

23 

38 

21871 

97579 

.23571 

.97182 

.25263 

.96756 

.26948 

.96301 

22 

89 

.21899 

97573 

.23599 

.97176 

.25291 

.96749 

.26976 

.96293 

21 

40 

.21928 

97566 

.23627 

.97169 

.25320 

.96742 

.27004 

.96285 

20 

41 

.21956 

.97560 

.23656 

.97162 

.25348 

.96734 

.27032 

.96277 

19 

42 

.21985 

.97553 

.23684 

.97155 

.25376 

.96727 

.27060 

.96269 

18 

43 

.22013 

.97547 

.23712 

.97148 

.25404 

.96719 

.27088 

.96261 

17 

44 

.22041 

.97541 

.23740 

.97141 

.25432 

.96712 

.27116 

.96253 

16 

45 

.22070 

.97534 

.23769 

.97134 

.25460 

.96705 

.27144 

.96246 

15 

46 

.22098 

.97528 

.23797 

.97127 

.25488 

.96697 

.27172 

.96238 

14 

47 

.22126 

.97521 

.23825 

.97120 

.25516 

.96690 

.27200 

.96230 

13 

48 

.22155 

.97515 

.23853 

.97113 

.2o545 

.96682 

.27228 

.96222 

12 

49 

.22183 

.97508 

.23882 

.97106 

.25573 

.96675 

.27256 

.96214 

11 

50 

.22212 

.97502 

.23910 

.97100 

.25601 

.96667 

.27284 

.96206 

10 

51 

.22240 

.97496 

.23938 

.97093 

.25C29 

.96660 

.27312 

.96198 

9 

52 

.22268 

.96489 

.23968 

.97086 

.25657 

.96653 

.27340 

.96190 

8 

53 

.22297 

.97483 

.23995 

.96079 

.25685 

.96645 

.27368 

.96182 

7 

54 

.22325 

.97476 

.24023 

.97072 

.25713 

.96638 

.27396 

.96174 

6 

65 

.22353 

.97470 

.24051 

.97065 

.25741 

.9S630 

.27424 

.96166 

5 

56 

.22382 

.97463 

.24079 

.97058 

.25769 

.96623 

.27452 

.96158 

4 

57 

.22410 

.97457 

.24108 

.97051 

.25798 

.96615 

.27480 

.96150 

3 

58 

.22438 

.97450 

.24136 

.9704-1 

.25826 

.96608 

.27508 

.96142 

2 

59 

.22467 

.97444 

.24164 

.97037 

.25854 

.96600 

.27536 

.96134 

1 

GO 

.22495 

.97437 

.24192 

.97030 

1.25882 

.96593 

.27564 

.96126 

0 

Iin7 

B 

A 

B 

~^~ 

1  B 

A 

B 

A 

Minr 

76°  75C 

READ  UP 
318 


Table  of  Angular  Ratio 


READ  DOWN 

16°  17° 


•L 

0 

.27564 

.96126 

.29237 

.30902 

.95106 

.32557 

.94552 

60 

i 

.27592 

.96118 

.29265 

.95622 

.30929 

.95097 

.32584 

.94542 

59 

2 

.27620 

.96110 

.29293 

.95613 

.30957 

.95088 

.32612 

.94503 

3 

.27648 

.96102 

.29321 

.95605 

.30985 

.95079 

.32639 

.94623 

57 

4 

.27676 

.96094 

.29348 

.95596 

.31012 

.95070 

.32667 

.94514 

56 

5 

.27704 

.96086 

.29376 

.95588 

.31040 

.95061 

.32694 

.94504 

6 

.277:;: 

.96078 

.29104 

.95579 

.31068 

.95052 

.32722 

.94495 

54 

7 

.27759 

.90070 

.2902 

.95571 

.31095 

.95043 

.32749 

.94485 

53 

8 

.27787 

.96062 

.29460 

-95562 

.31123 

.95033 

.32777 

.94476 

52 

9 

.27815 

.96054 

.29487 

.95.->54 

.31151 

.95024 

.32804 

.94466 

51 

10 

.27843 

.96046 

.29515 

.95545 

.31178 

.95015 

.32832 

50 

11 

.27871 

.96037 

.29543 

.95536 

.31206 

.95006 

.32859 

.94447 

II 

12 

.27899 

.96029 

.29571 

.95528 

.31233 

.94997 

.32887 

.94438 

48 

13 

.27927 

.96021 

.29599 

.95519 

.31261 

.94988 

.32914 

.94428 

17 

14 

.27955 

.96013 

.29626 

.95511 

.31289 

.94979 

.32942 

.'.'111* 

46 

15 

.27983 

.96005 

.29654 

.95502 

.31316 

.94970 

.32969 

.94409 

45 

16 

.28011 

.95997 

.29682 

.95493 

.31344 

.94961 

.32997 

.94399 

44 

17 

.28039 

.95989 

.29710 

.95485 

.31372 

.94952 

.33024 

.94390 

43 

18 

.28067 

.95981 

.29737 

.95476 

.31399 

.04943 

.33051 

.94380 

42 

10 

.28095 

.95972 

.29765 

.95167 

.31427 

.91933 

.33079 

.94370 

41 

20 

.28123 

.95964 

.29793 

.95459 

.31454 

.04924 

.33106 

.94361 

40 

21 

.28150 

.95956 

.29821 

.05450 

.31482 

.94915 

.33131 

.94351 

39 

22 

.28178 

.95948 

.29849 

.95441 

.31510 

.94906 

.33161 

.94342 

38 

23 

.28206 

.95940 

,.29876 

.95433 

.31537 

.94897 

.33189 

.94332 

37 

24 

.28234 

.95931 

.29904 

.95424 

.31565 

.94888 

.33216 

.94322 

36 

2--> 

.28262 

.95923 

.29932 

.95415 

.31593 

.94878 

.33241 

.94313 

35 

.28290 

.95915 

;29960 

.95407 

.31620 

.94869 

.33271 

.94303 

34 

27 

.28318 

.95907 

*29987 

.93398 

.31648 

.94860 

.33298 

.94293 

33 

28 

.28346 

.95898 

.30015 

.93389 

.31675 

.94851 

.33326 

.94284 

32 

29 

.28374 

.95890 

.30013 

.95380 

.31703 

.94842 

.33353 

.94274 

:;l 

30 

.2840-2 

.95882 

.30071 

.95372 

.31730 

.94832 

.33381 

30 

31 

.28429 

.95874 

.30093 

.95363 

.31758 

.94823 

.33408 

.94254 

29 

32 

.28457 

.95865 

.30126 

.9.">:>:>1 

.31786 

.94814 

.33436 

.Ol-2-i:. 

33 

.28485 

.95857 

.30154 

.95345 

.31813 

.94805 

.33463 

27 

34 

.28513 

.95849 

.30182 

.95337 

.31841 

.94705 

.94225 

35 

.28541 

.95841 

.30209 

.95328 

.94786 

.33518 

.04215 

36 

.28569 

.95832 

.80087 

.95319 

.31896 

.01777 

.33545 

.94206 

M 

37 

.28597 

.95824 

.30265 

.95310 

.31923 

.94768 

.33573 

.94196 

28 

38 

.28625 

.95816 

.30292 

.95301 

.31951 

.94758 

.33600 

,94186 

22 

39 

2MB9 

.95807 

.30320 

.95293 

.31979 

.'.'1719 

.33627 

.94176 

21 

40 

.28680 

.95799 

.30348 

.95284 

.32006 

.94740 

.33655 

'.'lir,7 

20 

41 

2871  - 

.0,-)791 

.30376 

.95275 

.32P34 

.94730 

19 

42 

.28736 

.95782 

.30403 

.95206 

.32061 

.94721-.  33710 

.-.'11  17 

18 

4:: 

.  9704 

.95774 

.30431 

.95257 

.32089 

.94712 

17 

44 

.28792 

.95766 

.30459 

.32116 

.94702 

.33764 

'.H127 

16 

45 

.28820 

.95757 

.30486 

.95240 

.:!2l4l 

.94118 

II 

46 

.28847 

.95749 

..30514 

.95281 

.32171 

.94108 

14 

47 

.28875 

.95740 

.95222 

.32199 

.33846 

;  - 

n 

48 

.28903 

.30570 

.95213 

.32227 

.94665 

.33874 

.94068 

u 

49 

.28931 

.'.'5721 

.£0597 

.95204 

.32254 

u 

50 

.28959 

.'.'.-.7i:. 

.3062.-, 

.32282 

10 

51 

.28987 

.95707 

.95186 

.32309 

•!'  * 

.94058 

i 

U  .306SO 

.04627 

.94049 

I 

.20012 

.95690 

.30708 

.32364 

.94618 

.34ull 

.   • 

7 

.29070 

.95681 

.95159 

.32392 

.94669 

.9402V 

1 

55 

.29098 

.95673 

.96150 

.::-2ll'J 

' 

.94019 

" 

56 

.29126 

.96664 

.94590 

. 

4 

.'201  .VI 

.94580 

.93999 

.. 

58 

.29182 

.95647 

.30846 

.32502 

.94571 

.9?989 

2 

.29209 

.9.5639 

.30874 

.32529 

.93979 

1 

M 

.29237 

.95630 

.30902 

.95106 

••!•  : 

,  .. 

1 

—  m~ 

A 

• 

A 

~~j 

* 

B 

A 

IT 

'  - 

3° 

7 

I 

7 

«' 

;  i  U 

>  UP 

319 

Table  of  Angular  Ratio 


20° 

READ  DOWN 
21° 

22° 

23° 

0 

.34202 

.9396<: 

.  35837  1.93358  '.37461 

.92718 

.  39073 

B   Min. 
1.92050  60 

1 

.34228 

.9395'J 

.35864  '.93348  .37488 

'.92707 

.39100 

.92039  59 

2 

.34257 

'  .  93949  !  !  .  3589  1  '  .  93337  :  .  37515 

.92697 

.39127 

.92028;  58 

3 

.34284 

.93930  ]  .35918  .93327  '  .37542 

.92686 

.39153 

.92016  57 

4 

.34311 

.93929'  .35945  .93310  '.37569 

.92878 

.39180 

.92005'  56 

5 

.34339 

.93913 

j:.  35973  '.9330G  .37.VJ5 

.92664 

.39207 

.91994  55 

6 

.34?  66 

.93909 

.300001.93295  .37622 

.92653 

.39234 

.91982  54 

7 

.34393 

'.93899 

.36027  .93285  .37649 

.92612 

.39260 

:.91971  53 

8 

.34421 

.93889 

.30054  .93274  ..37676 

.92631 

.392S7 

1-91959:  52 

0  .34448 

|.  93879 

.36081  .93264  .37703 

.92620 

.39314 

.91948  51 

10  .34475 

.93869 

.36108  .  93253  .37730 

.92609 

.39341 

.91930  50 

11  .34503 

'.93859 

.36135  .93243  i.  37757 

.92598 

.39367 

.91925  49 

12  i.  34530 

.93849 

.36162  .93232  .377*4 

.92587 

.39394 

.91914  48 

13  .34557 

.93839  '.S6190  .93222  .37811  .92576 

.39421 

.91902  47 

14 

.34584 

.93829 

.36217  .93211  .37838 

.92505 

.39448 

.91891  46 

15  .34612 

.93819 

.36244  .93201  i.  37865 

.92554 

.  39474 

.91879  45 

16  .34639 

.93809 

!'.  36271  '.93190  1.37892 

.92543 

.39501 

.91868  44 

17  .34666 

.93799 

.36298  .93180  ;.  37919 

.92532 

.89528 

.91856 

43 

18  1.34694 

.93789 

.36325  .93169  '.37946 

.92521 

.39555 

.91845  42 

19  .34721 

.93779 

.36352  .93159  :.  37973 

.92510 

.39581 

.91833 

41 

20 

.34748 

.93769 

.36379  .93148  i.  37999 

.92499 

.39008 

.91822 

40 

21 

.34775 

.93759 

.36406  .93137  '.38026 

.92488 

.39635 

.91810 

39 

22 

.34803 

.93748 

.36434  .93127  .38053 

.92477 

.39001 

.91799  38 

23 

.34830 

.93738 

.36461  .93110  1.38080 

.92466 

.39688 

.  91787  j  37 

24 

.34857 

.93728 

.36488  .93106  i.  38107 

.92455 

.80716 

.91775  36 

25 

.34884 

.93718 

.30515  .93095  .38134 

.92444 

.39741 

.91764!  35 

26 

.34912 

.93708 

.30542  .93084  .38161 

.92432 

.39768 

.91752  34 

27  .34939 

.93698 

1  .36569  .93074  .38188 

.9242J. 

.39796 

.91741 

33 

28  .34966 

.93688 

.36596  .93063  ^.38215 

.92410 

39822 

.91729  32 

29 

.34993 

.93677 

.36623;-  93052  .38241 

.92399 

.39848 

.91718  31 

30  .35021 

.93667 

.36650  .93042  .38268 

.92388 

.39875 

.91706  30 

31  .35048 

.93657 

.36677  .93031  .38295 

.92377 

.39902 

.91694 

29 

32 

.35075 

.98647 

.30704  .93020  :.  38322 

.92366 

.39928 

.91683 

28 

33 

.35102 

.93637 

.30731  .93010  '.38349 

.92355 

.39955 

.91671 

27 

34 

.35130 

.93626 

.3(57  58  '.92999:1.  38376 

.92343 

.39982 

.91660 

26 

36 

.35157 

.93616 

.  36785  -  92988  .38403 

.92332 

.40008 

.91648 

25 

36 

.35184 

.93606 

.36812  .92978  .38430 

.92321 

.40035 

.91636  24 

37 

.35211 

.03596 

.  36839  ;.  92967  .38456 

.92310 

.40062 

.91025  23 

38 

.35230 

.93585 

.36867  .92956  .38483 

.92299 

.40088 

.91013  22 

39 

.35266 

.93575 

.308941.92945  .38510 

.96287 

.40115 

.91601  21 

40 

.35293 

.93C65 

:.  36921  1.92935  .38537 

.92276 

.40141 

.91590  20 

41 

.35320 

.93555 

.36948  .92924.  '.38564 

.92265 

.40108 

.91578|  19 

42 

.35347 

.93544  I.  36975  i.  92913  .38591 

.92254 

.40195 

.91566  18 

43 

.35375 

.  93534  {  1  .87002  1  •  92902  .  3801  7 

.92243 

.40221 

.91505 

17 

44 

.35402 

.93524 

.37029  -928&2  .38644 

.92231 

.40248 

.91543 

16 

45 

.35429 

.93514 

.37056  .92881  .  38071  .92220 

..1027.-. 

.91531 

15 

4C 

.35456 

.93503 

.37083  .92870  .38698 

.92209 

.40301 

.91519  14 

47 

.35484 

.93493 

.37110!.  92859  .38725 

.92198 

.40328 

.91508  13 

48 

.35511 

.93483 

'.37137  .92849  .38752 

.92186 

.40355 

.91496 

12 

49 

.35583 

.93472 

.37164  .92838  .88778 

.92175 

.4(1381 

.91484 

11 

50 

.35565 

.93462 

i.  37191  :.  92827  .38805 

.92164 

.40408 

.91472 

10 

51 

.35592  .93452 

.37218  .92810  .38832 

.92152 

.40434 

.91461 

9 

52 

.35619 

.93441 

.37245  .92805  1.38859 

.92141 

.40401 

.91449 

8 

53 

.35647 

.93431 

.37272  .92794  .38886 

.  92130 

.4IU8.8 

.91437 

7 

54 

.35674 

.93420 

.37299  .92784  .3S'.U2 

.92119 

.40511 

.91425 

6 

55 

.35701 

.93410 

.37326  .92773  '38939 

.92107 

.40643 

.91414 

5 

56 

.35728 

.93400 

.37353  .92762  i.  38966 

.92096 

.  40567 

.91402 

4 

57 

.35755 

.93389 

.37380  .92751  .  38993 

.92085 

.40594 

.91390 

3 

58. 

.35782 

.93379 

.37407  .92740  .  39020 

.92073 

.40621 

.91378 

2 

59 

.35810 

.93368 

.87434  .!>272<>  .39046 

.92062 

.40047 

.91366 

1 

60  .35837 

.93358 

.37401  .92718  .3907:! 

.92050 

.40674 

.'.H355 

0 

jfc_!_m_. 

A 

B     A   •   B 

A 

B 

A 

lii' 

« 

9° 

68° 

7° 

t 

(6° 

READ  UP 

320 

Table  of  Angular  Ratio 


24° 

READ   I  >o\VX 
25°                     26° 

27° 

0 

.40674 

.91335 

.42262   .90631 

.43837  '.89879 

.45399 

.89101 

'', 

1 

.40700 

.91343 

.4228S  .90618 

.43863  .89867 

.45425 

.89087 

59 

2 

.40727 

.91331 

.42315  .90606 

.43889  .89854 

.45451 

90074 

H 

3 

.40753 

.91319 

.42341  .90594 

.43916  '.89841 

57 

4 

.40780 

.91307 

.42307  .90582 

.i:;'.'l.'  .^.ivJS 

.45503 

.8M48 

56 

5 

.40806 

.91?.i.-«    .42397  .90569 

.43968  '.89816 

.45529 

.89035 

55 

6 

.40833 

.42420 

.90557 

.43994  .89803 

.45554 

.89021     M 

7 

.40860 

.91272 

.42446  .90545 

.44020  |.  89790 

.45580 

.89008,  53 

8 

.40386 

.91260 

!.  42473  .90532 

.44046  .89777 

.4560(3 

9 

.40913 

.91218 

.42499   .90520 

.44i>72   .89704 

.  1.--632 

.88981    51 

10 

.40939 

.91236 

.42525  .90507 

.44098  '.89752 

|  .45658 

.88968    50 

11 

.40966 

.91224 

.42552  .90495 

.44124  .89739 

.45684 

.88955    49 

12 

.40992 

.91212 

.42578  .90483 

.44151  .89726 

.45710 

.88942 

1- 

13 

.41019 

.91203 

.42004   .90470 

.44177  .89713 

.45736 

-:•_- 

47 

14 

.41045 

.91188 

'.426311.90458 

.44203  .89700 

.45702 

.88915    46 

15 

.41072 

.91176 

.42657  '.90446 

.44229  .89687 

.45787 

16 

.41098 

.91164 

.42683  .90433 

.44255  .89674 

.45813 

.88888    44 

17 

.41125 

.91)52 

.42709  .90421 

.44281  .89662 

.45839 

.88875    43 

18 

.41151 

.91140     .42736  .90408 

.44307  .89649 

.45865 

.88862    42 

19 

.41178 

.'.'1128    .42762  .90396    .44333,  .89636 

.45891 

20 

.41204 

.91116 

.42788  '.90383 

.44359  .89623 

.45917 

.88835    40 

21 

.41231 

.91104 

.42815  .90371 

.44385  .89610 

.45942 

.88822    39 

22 

.41257 

.91092 

.42841 

.90358 

.44411   .89597 

.45968 

.88808 

38 

23 

.41284 

.91080 

.90446 

.44437  .89584 

.45994 

.88795 

37 

24 

.41310 

.91068 

.42894 

.90334 

.44464  .89571 

.46020 

.88782 

36 

25 

.41337 

.91056 

'.42920  .90321 

.44490  .89558 

.46046 

--:•  - 

35 

26 

.41363 

.91044 

.42946L  90309 

.44516  .89545 

.46072 

.88755 

34 

27 

.41390 

.91032 

.42972   .902% 

.44542  .89532 

.46097 

.88741 

33 

28 

.41416 

.91020 

.42999 

.90284 

.44568  .89519 

.46123 

VOX    •  '- 

29 

.41443 

.91008 

.43025  .90271 

.44594    89506 

.46149 

.NS71".     31 

30 

.41469 

.90996 

.43051  .90259 

.44620  .89493 

.46175 

.88701     30 

31 

.41496 

.90984 

.43077  .90246 

.44646  .89480 

.46201 

.88688    29 

32 

41522 

.90972 

'.43104 

.90233 

.44672  .89407 

.46226 

33 

.41549 

.90960 

.43130  .90221 

.44698  .89454 

.46252 

.8S661    27 

34 

.41575 

.90948 

.43156  .90208 

.44724   .89441 

.46278' 

35 

.41002 

.90936 

'.43182 

.90196 

.44750  .89428 

.46304 

36 

.41628 

.90924 

.43209 

.90183 

.44776  .89415 

.46330 

37 

.41655 

.90911 

.43235 

.90171    .44802  .89402 

.46355 

-..- 

23 

38 

.41681 

.90899 

.43261 

.90158  1'.  44828  .89389 

.46381 

.88593 

22 

39 

.41707 

.90887 

.43287 

.90146 

.44854;.  89376 

.46407 

.88580 

21 

40 

.41734 

.90875 

.43313 

.90133 

.  44880  !.  89363 

.46433 

.88566 

20 

41 

.41700 

.90863 

43340 

.90120    .44906  .89350 

.46458 

.88533 

19 

42 

.417*7 

.9H851     .43366 

.90108 

.54932  .89337 

.46484 

•-:,    • 

18 

43 

.41813 

.90839 

.43392 

.90095 

.44958  .89324 

.46510 

.88526 

17 

44 

.41840 

.43418 

.90082 

.46536 

.88512 

16 

45 

.41866 

.90814 

.43445 

.90070 

.45010  .89298 

.46561 

15 

46 

.41892  .90802 

.43471 

.90057 

45036  .89285 

.46587 

.88485 

14 

47 

.41919 

.90790 

.43497 

.90045 

.45062 

.46613 

.88472    13 

48 

.41945 

.90778 

.43523 

.90032 

.45088  .*'.'. 

49 

.41178 

.90766 

.yotil'j      i:>H4  .89245 

.46664 

50 

.90753 

.43575 

.90007 

.45140  .89232 

.46690 

.88431     10 

51 

.42024 

.90741 

.43602 

.....; 

.45166  .WJl«j 

.46716 

.88417 

9 

52 

.42051 

.90729 

.43628 

.89981    .45192  .89206 

.46742 

.88404 

8 

53 

.42077 

.90717 

.43654 

.89968 

.46767 

.88390 

7 

54 

.42104 

.90704 

.4tftt> 

.89956 

.45243  .89180 

.46793 

.88377 

6 

55 

.42130 

.90692 

.43706 

.89943 

56 

.42156 

.90680 

.43733 

.88M9     4 

57 

.42183 

.90668 

.43759 

.89918 

.45321   .89140 

.46870 

3 

58 

.42209 

.90655 

.89905 

46896 

-.    / 

2 

59 

.42235 

.90643 

.43811 

.89892 

I',::::     --'li! 

.46921 

-     - 

1 

60 

TST 

.42262 

.90631 

A 

!.  43837 

• 

"  A 

i.vr-    -•:<: 

;-i~nr 

IT  — 

0 

B 

>°    ' 

«;:i 

«- 

.BEAD  UP 

821 

Table  of  Angular  Ratio 

READ  DOWN 
28°  29°  30°  31° 


Min. 

Mm. 

0 

.46947  .88295 

.48481 

.87462 

.50000 

.86603 

.51504 

.85717 

60 

1 

.469731.88281  .48506  .87448 

.50025 

.86583 

.51529 

.85702 

59 

.469991.88267  .48532  '.87434 

.50050 

.51554 

.85687 

58 

3 

.470241.88254  1.48557 

.87420 

.50076 

'.86559 

.51579 

.85672 

57 

4 

.  47050  j.  88240  .48583 

.87406 

.50101 

.86544 

.51604 

.85657 

M 

5 

.47076  !  .88226 

.48608 

.87391 

.50126 

.86530 

'.51628 

.85642 

5B 

f, 

.47101  .88213 

.48634  .87377 

.50151 

.86515 

.51653 

.8-5627 

54 

7 

.47127 

.88199  1.48659  .87363 

.50176 

.86501 

.51678 

.85612 

68 

- 

.47153 

.88185  1.48684 

.87349 

.50201 

.86486 

.51703 

.85597 

52 

B 

.47178 

.88172'  .48710 

.87335 

.50227 

.86471 

j.  51728 

.85582 

51 

10 

.47204  .88158  .48735 

.87321 

.50252 

.86457 

1.51753 

.85567 

50 

11 

.47209  L88144  .  4*761 

.87306 

.50277 

.86442 

.5177* 

.85551 

49 

12 

.47255  .88130  .48786 

.87292 

.50302 

.86427 

'.51803 

•85536 

4^ 

i:; 

.47281 

.88117  .48M1 

.87278 

.50327 

.86413 

.51828 

.85521 

47 

14 

.47306 

.88103  .48837 

.87264 

.50352 

.86398 

!.  51852 

.85506 

46 

15 

.47332 

.880891  .48862 

.87250 

.50377 

.86384 

.51877 

.85491 

45 

16 

.47358 

.88075  1.48888  .87235 

.50403 

.86369 

.51902 

.85476. 

44 

17 

.47383 

.88062  i.  48913  .87221 

.50428 

.86354 

.51927 

.85461 

43 

U 

.47409 

.88048  '.48938 

.87207 

.50453 

.86340 

.51952 

.85446 

42 

IS 

47434 

.88034  '[.48964 

.87193 

.50478 

.86325 

.51977 

.85431 

a 

•JO 

.47460 

.88020  .48989 

.87178 

.50503 

.86310 

.52002 

.85416 

10 

•21 

.47486 

.8SOC6  .4*014 

.87164 

.50528 

.96295 

L  52026 

.85401 

39 

22 

.47511  .87993:  .49040  .87150 

.50553 

.86281 

1.52051 

.85385 

88 

28 

47537  .87979;  .49065  .87136 

.50578 

.86266 

.52076 

.85370 

37 

24 

47562  .87965  I1.  49090  .87121 

.50603 

.86251 

.52101 

.85355 

M 

25 

.47588 

.87951 

1.49116  .87107 

.50628 

.86237 

.52126 

.85340 

88 

26 

.47614 

.87937 

.49141 

.87093 

.50654 

.86222 

.52151 

.85325 

34 

27 

.47639 

.87923 

1.49166  .87079 

.50679 

.86207 

.52175 

.85310 

88 

28 

47665 

.87909 

1.49192  .87064 

.50704 

.86192 

.52200 

.85294 

32 

29 

47690 

.87896 

.49217  .87050 

.50729 

.86178 

.52225 

.85279 

31 

80 

47716 

.87882 

.49242  .87036 

.50754 

.86163 

.52250 

.85264 

80 

31 

47741 

.87868 

.49268  .87021 

.50779 

.86148 

.52275 

.85249 

28 

32 

47767 

.87854 

.49293  .87007 

.50804 

.86133 

.52299 

.8BBM 

28 

:•;:; 

47793 

.87840 

.49318  .86993 

.50829 

.86119 

'.52324 

.85218 

27 

34 

.47818 

.87826  i.  49344  .86978 

.50854 

.86104 

.52349 

.85203 

26 

36 

47844 

.87812  .49369  .86964 

.50879 

.86089 

1.52374 

.85188 

• 

96 

.47869 

.87798  .493941.86949 

.50904 

.86074 

.52399 

.85173 

24 

37 

.47895  .87784 

.494191.86935 

.50929 

.86059 

.52423 

.85157 

23 

88 

.47920  .87770  .  49445  |.  86921 

.50954 

.86045 

.52448 

.85142 

22 

39 

.47946 

87756 

.49470 

.86906 

.5C979 

.86030 

.52473 

.85127 

21 

40 

.47971 

.87743 

.49495 

.86892 

.51004 

.86015 

,.52498 

.85112 

20 

41 

.47997 

87729 

.49521 

.86878 

.51029 

.86000 

.52522 

.85096 

1'J 

42 

.48022 

87715 

.49546 

.86863 

.51054 

.85985 

.52547 

.85081 

18 

43 

.48048 

.87701 

.49571 

."86849 

.51079 

.85970 

.52572 

.86060 

17 

•14 

^8073 

.87687 

.495% 

.86834 

.51104 

.85956 

.52597 

.85051 

u 

45 

.48099 

.87673 

.49622 

.86820 

.51129 

.85941 

.52021 

.85035 

ft 

46 

.48124 

.87659 

.49647 

.86805 

.51154 

.85926 

.52646 

.85020 

14 

47 

.48150 

.87645 

.49672 

.86791 

.51179 

.85911 

!.  52671 

.85005 

U 

•IS 

.48175 

.87631 

.49697 

.86777 

.51204 

.858% 

.526% 

.84989 

12 

49 

.48201 

.87617 

.49723  .86762 

.51229 

.85881 

.52720 

.84974 

11 

50 

.48226 

.87603 

.49748  .86748 

,.51254 

.85866 

.52745 

.84959 

10 

51 

.48252 

•87589  !.  49773  [.86733 

.51279 

.85851 

.52770 

.84943 

9 

52 

.48277 

.  87575  1  .49798  .86719 

.51304 

.85836 

.527'J-l 

.84928 

8 

53 

.48303 

.87561 

.49824 

.86704 

.51329 

.85821 

;.  52819 

.84913 

7 

54 

.48328 

.87546 

.49849 

.86690 

.51354 

.85806 

.52844 

.84897 

6 

55 

.48354 

.87532  [.49874  .86675 

.51379 

.85792 

.52809 

.84882 

5 

56 

.48379 

.  87518  jj.  49899;.  86661 

'  .51404 

.85777 

.52893 

.84866 

4 

57 

.48405 

.87504 

.49924  .86646 

.51429 

.25762 

j.  52918 

.84851 

3 

68 

.48430 

.87490 

!.  49950  .86632 

.51451 

.85747 

.52943 

.84836 

2 

n 

.48456 

.87476 

'.49975  .86617!  1.51479 

.85732 

.52%7 

.84820 

1 

Ml 

.48481 

.87462 

.50000  .86603 

.51504 

.85717  .52992  .84805 

0 

"Min. 

~B~ 

A 

~B     A~ 

i~T~ 

I~A~ 

B 

nr 

1W." 

60°  59° 

READ  UP 


Table  of  Angular  Ratio 


32° 


35° 


0  1.52992 
.53017 
.53041 
.53066 
.53091 
.53115 
.53140 


.84805|  .54464 

.84771     .54.--1:; 
.84759,  |.54;37 


.84743 
.84728 
.84712 


83819 
545f,l.  83804 


83835:  .55908 


.54586 


MMG 


.53189  .84681 
.53214  .84666! 

.53238J.84650    .54708 
84635' 


.53337 


84573 


83740 
83724 


83676 
83660 


.55992 
.56016 
.56040 
.56064 
.56088 
.56112 
.56136 
.56160 
.56184 


.82904 


.67381 
j.  57405 

•7429 


.81915 
.81899 


na 


82839 


.57453 |.81848 
.57477  >lx,2 
.57501^.81815 
.57524  .81796 


.57572 


.54805  .83645  !. 56266 


.51829    88021 


53435 


53484 
53509 


M5.-7     .648S4 

84542     .54878 
S452C     .51902 


.84495 
,84480 


.54975 


53534  .84161    ..Jl'J'i'J 
.53558 j.84448    .55024 
84433  H.  55048 

81417     .55072 
84402 ';. 55097 
55121 


53607 
53C32 


.um 


82708  1.57643 

.57667 


:82692Ji 


- 


.81782 
.81765 
.81748 
.81731 
.81714 
.81698 
JUH 


.8261:$ 


.56353  .82610 j, 
.56377  .82593 
.56401  . 82577 j! 


.56425 
.56449 


.82561 
.82544 


,84370 

537051.84355 
53730  .84339 

53754  .84324 j !. 55218 j. 83373 
53779  .84308: 


MM 

83453J 
83437 

.55145  .83421 
83405 

55194L 83389 


.57715  .81661 

.5770.2  .81031 
.57786  .81614 
.57810  .81597 
.57833  .81580 
.57857  .8156.-5 
.57881 '.81546 
.57904  .81530 
.57928 '.81513 


53804 1 .84292! 
84277 


.55266 
.55291 


53951 
53975!.  84182 
54000  .84167 
54024  .84151 
54049  .84135 
54073 ' 

84104 


MOB 


84261  .55315 

84245  1.55339 

84230  1.55363 

84214  .55388 

84198  .55112 


54293 


54366 


51161 


-I  9Q 


9016 


ma 


.55436 
.55460 


.55509 


.55557 
.55581 

.55630 
.55654 


.55726 


.55799 


.55847 


BUM 


.83179 
.83163 
.83147 


.56497  I. S2T.  11 

.56521 '.82495    .57952  .814% 
.56545  .82478 
.82462 


.57'.i7f. 


nui 


57999 


.56617 

.56641  .82413 
.  56665 1. 82396 1 
82380; 
.56713 

.56736  .82347; 
.56760 
.56784 

.82281  . 


.81479 


.81462 


.56880  .82248 
'.56904  .82231 
'.56928  • 
. 56962  I.82198J'. 68378 

Ml 
MM 


81445 
58047  .81428 
58070 1.8)412 
58094 '.81395 
68118  .81378 
.r.si4l  >l:;01 
58165  .81344 
58;89  .81327 
582121.81310 
58236  .81293 
58260  .81276 
58283  .81359 
,-.;.•:  .fUll 


.57000 '.82165 
.57021  .R.M4K 
.57047  .82132 


•    ••  • 


.57071 
.57095 
.57119 

SI50I7     .571H1 
.5721,'. 

MM 
MM 


IBM 


MM 

tan 


B21J  • 


Hi  • 

M  • 
MM 
MM 


MM 


M 


MM 


Ml  :  • 
Ml  I 


:.-..:; 

Ml  • 


Ml  I 

81191 

81174 

81167 

81140 

81123 

81106 

-     - 

81072 

81055 

H    | 

81021 

81004 

MM 


Table  of  Angular  Ratio 


BEAD  DOWN 
37°        5 


. 62932 '. 777 IS 
. 62955 !.7769C 
. 62977 I.77G7S 
.6:5000  .77060 
.63022  .77611 
.63045  .77623 
.63068|.77605 
. 63090 '.775SG 
.631131.77568 
.63135  .77550 
.63158  .77531 
.63180 '.7751 3 
.03203  .7749! 
.C-::i;±')  .77171 
.63248  .77458 
.63271  .77430 
.63293 ,.77421 
. 63316 !. 77402 
.63338|.77384 
.63361  .77301! 
.63383  .77347 
.63406 '.77329 
. 63428 j. 77310 
.63451  .77292 
.63473  .77273 
. 63496 L 77255 
1-63518  .77236 
'. 63540 . 77218 
. 63563 !. 77199 


59084 
59108 
59131 
59154 

59178 


8514 
.61955  .78496 
.61 978 |.78478 
.62001  .78460 
.620241.78442 
.78424 
.78405 

62092 
.62115  . 
.62138;. 78351 
. 62160 ' 
.62183J.78315 
.62206  .78297 
,62229  [.78279 
. 62251 !. 78261 
.62274  .78243 

02297 
.62320J.78206 
.62342  .781881 
.62365 1.78170 


69225 

59248 
59272 
59295 
59318 
59342 
59365 


-,9552 

.Y.I: 

5U599 

B9622 

6964C 


62456 

62479L78079 
625021.78061 


79176 
79158 
79140 
79122 
79105 
79087 


80195 
80178 
80160 
80143 
80125 
80108 


62524 

62547 
62570 
62592  .779SS 
62615 j. 77970 
62638 j. 77952 
62660 '.77934 
62683  .77916 
62706 '.77897 
62728:. 77879 
62751  .77861 
62774 
62796  .778241 
9  .77806 


.61153 
.61176 
.61199 
.61222 
.61245 
.61268 
.61291 
.61314 


_  6847 
64011  .7682? 
64033 '.76810 
6405C 

C,  107:- 


61190  .7007'.) 
64212  .76661 
64234!. 76642 
64256  .76623 
64279  .76601 


Table  of  Angular  Ratio 


READ  D3WN 

41°  42° 


43° 


MC 
0 

.64279 

.76604; 

'.65606 

.75471 

.66913 

-±_||_A_|_B_ 
.74314    .08200  .73135 

•to. 
60 

1 

.64301 

.76686 

j.  65628 

.75482 

68085 

-7.12-.i5     .6S221   .73116 

59 

2 

.64323 

.76567 

.65650 

.75433    .66956 

-242  .73096 

58 

3 

.64346 

.76548 

.65672 

.75414    .66978 

•.-264   .7?07G 

57 

4 

.64368 

.76530 

.65694 

.75395    .00999 

-285  .73056 

56 

5 

.64390 

.76511 

.65716 

.75678 

.67021 

-306  .73036 

55 

6 

.64412 

.76492 

.65738 

.75356 

.67045 

-  127  .78016 

54 

7 

.64435 

.76473  |.  65759 

.75337 

.67064 

.7117s    .-,- 

53 

8 

.64457 

.76455 

i.  65781 

.75818    .67086 

.74159     .68370  .72970 

9 

.64479 

.76436 

.65803 

.75299    .67107 

-::91   .72957 

51 

10 

.64501 

.76417 

.65825  .75280    .67129 

.74120    .68412   .72937 

M 

13 

.64524 

.  7G39S 

.65M7   .75261     .67151 

.74100    .68434  .72917 

49 

12 

.64546 

'.65869  .75241 

.07172 

.740SO    .  68455  !.  72897 

H 

ia 

.'64668 

.76361 

.67194 

-i76   .72S77 

47 

14 

.64590 

.76342 

.65913 

.75203 

.67215 

.74041  1  .  681'.  >7  .72887 

46 

15 

.64612 

.76323 

.65935 

.75184    .67232 

.74022!  .09 

45 

ie 

.64635 

.76304 

L  65956 

.75165    .67258 

.74002    .68539  .72817 

44 

17 

.64657 

.  76286  : 

.65978 

.75146  '.67280 

.  73983  j  .68561  .72797 

43 

18 

.64679 

.76267 

.66000 

.75126 

i.  67301 

.73963    .68582  .72777 

12 

10 

.64701 

.76248 

.66022 

.75107 

.67323 

-6"3   .7-757 

41 

20    .64723 

.76229 

.66044 

.75088  1.67344 

-«i24  .72737     40 

21    .64746 

.76210 

.66066 

.75069'   .07366 

.73904  1.68045  .72717 

39 

22 

.64768 

.76192 

.66088 

.75050 

.67387  !  .73885    .68666  \  .72697 

38 

23 

.64790 

.76173 

.66109 

.75030 

.67409 

-.  -,88  .72677 

37 

24 

.64812 

.76154 

.66131 

.75011    .67430 

.7:MO    .68709  .72657 

36 

25 

.64834 

.76135 

.60153 

.71992    .67-152 

.08730  .726^7 

35 

26 

.64856 

.7611G 

.66175 

.7-1973    .67473 

-751   .72017     31 

27 

.64878 

.76097 

.00197  .74953    .67495 

33 

28 

.64901 

.76078 

.66218  j.74934     .07516 

.73707     .68793  .72577 

32 

2fl 

.64923 

.76059 

.66240.74915    .675:1* 

.73717     .GSS11   .72557     :U 

80 

.64945 

.76041 

.66262  .74896    .67559 

.73728    .68835  .72 

31 

.64967 

.70022 

.662841.74876    .67580  .73708    .68*57  .72517     29 

83 

.64989 

.76003 

.66306  .74857    .67002 

.73688    .68878.72 

;,., 

.65011 

.75984 

.60327  .74838 

.670-3 

.73069    .6SS99  .72177     27 

34 

.65033 

.75965 

.66349 

.74818 

.07615 

.73019     .OVJ20   .72157     20 

85 

.65055 

.75946 

.66371 

.74799 

.67666 

88 

.65077 

.76827 

.66898  .74780 

.67688 

.73010     .6*962   .72117 

24 

87 

.65100 

.75908 

.66414 

.74760 

23 

88 

.65122 

.75889 

.66486 

.74741 

.67730 

.73570    .09004  .72377 

22 

:.-.' 

.65144 

.74722 

.  GTTo'J 

.73551     ,0.< 

21 

i  • 

.65166 

.75861 

.66480 

.74703    .67773 

20 

u 

.65186 

.66501 

.7:1511    .1. 

19 

42 

.65210 

.75813 

.66639 

.7KX-.1     .07*10 

.73191     .0'.' 

18 

48 

.65232 

.7579-1 

.66546 

.74644    .67887 

.73-172    .i9109  .72277 

17 

44 

.65254 

.75775 

.6<;:>«;6  .710-5    .67860 

180   .72-57 

16 

45 

.65276 

.75756 

- 

.73132      0   : 

15 

46 

.69088  .757:o 

.66r,;u  .71 

.7:;  113     .i'.9  172  .72216 

14 

47 

.65320  .75719, 

.C,(,032  .71507     .67923 

1193  .721-.-0 

18 

48 

.65342  .75700 

•Jit   .72176 

12 

!•• 

.65364  .75680 

.66675  .745 

11 

• 

.65386 

.75001 

.66697 

10 

61 

.65408 

.75012 

.66718 

a  16 

52 

.65430 

.7562; 

.(•,6710  .744' 

.65452 

.75604 

.66762  .7i; 

I  ; 

.65474 

.  :i     .os<i72 

.-. 

.65196 

.7,5566 

.66805 

66 

.65518 

.75517 

.66827 

57 

.65540 

.66848 

58 

.65562 

.75509 

.78178    .6  : 

H 

.65584 

.7549") 

60 

.656C6 

.75,7, 

ri934 

Table  of  Angular  Ratio 


T.EAD  DOWN 

4-1° 


.  7193-1 

.71914 


.C9529 
. 69549 j 
.69570 
.09591 
.09612 


.69654 
.69675 


.69717  .71691 
,69737  .71671 
,69758  .71650 


.71590 
.71569 


1  A 


T: 


.70132 
.70153 
.70174 
.70195 
.70215 
.70236 


1468 
,71447 
,71427 
,71407 
,71386 
,71366 
.71315 
,71325 
71305 
71284 
71264 
71243 
,71223 
71203 
71182 
,71162 
71141 
71121 


45° 
READ  UP 


70381 

70101 
70422 
70141! 
7046:'- 
70484 
70505 
70525 | 
70516 
70567 
705S7 
7100* 
70628 1 
706491 
70670 
70690 ! 
70711 


INDEX. 


PAGE. 

Explanation  of  Table  of  Reductions  and 
Squares, 1 

Explanation  of  Column  of  Squares,    .     .       2 
Tabular  Difference,      .......       3 

Table  of  Reductions  and  Squares,    .     5  to  304 

Table  of  Pitches  per  Foot, 305 

Table  of  Angular  Ratios, 314 


THE  LIBRARY 
UNIVERSITY  OF  CALIFORNIA 

Santa  Barbara 


THIS  BOOK  IS  DUE  ON  THE  LAST  DATE 
STAMPED  BELOW. 


Series  9482 


A    000588278 


w?m 


Mi 


raw 


m 


Hi 


BHHB 


1 


